Defining Communication
 The Communication Standard | Using Effective Questioning | Using Precise Language | Additional Communication Strategies | Communication and the Other Process Standards | The Classroom Environment | Summary | Your Journal

Questioning by a teacher can help students think through a problem and communicate coherently so that they truly come to understand their own reasoning and problem-solving processes. Questioning is one of the best ways for teachers to learn what students are thinking. If students are having difficulty, effective questions can help them figure out their mistakes and then correct the mistakes on their own. Sometimes all a teacher needs to do is ask generic questions, for example:

• What are you working on?
• What are you being asked to do?
• Are there words you don't understand?
• Will drawing a picture help?
• Is this similar to a problem you've seen before?
• What have you done so far?
• Where are you stuck?

If the teacher is trying to get across a particular concept, then the questions might be more directly tied to the specifics of the mathematical idea or the ways that the students are thinking about it. Let's take another look at the Fraction Tracks game introduced earlier in this session in the Observe Viewer activity.

 The student said, "I drew a card with the fraction 8/8 on it. I don't know what to do, since I can't use 8/8 on either the fourths or the eighths track."

Below is a series of questions you might ask this student. For each question, think about an answer the student might provide, then select "Show Answer" to see another possible answer the student might give. Decide for yourself whether you think the questions were effective.

 Teacher: Why can't you use the entire 8/8 on either of the tracks? Show Answer
 Student: I can't use 8/8 on the fourths track because there's already a marker on 1/4, and I can't use 8/8 on the eighths track because there's already a marker on 2/8.
 Teacher: Can you use part of the 8/8 on either track? Show Answer
 Student: Yes.
 Teacher: How much could you use on the fourths track? Show Answer
 Student: The marker's at 1/4, so I could use 3/4.
 Teacher: What is 3/4 equivalent to on the eighths track? Show Answer
 Student: It's also 6/8, so I could use 6/8 on the eighths track.

In order to set the stage for successful communication in mathematics, the questions the teacher asks should help students clarify and extend their thinking without telling them how to do the problem. This allows students to make sense of the mathematical ideas, which then strengthens their understanding of the concepts. So, how does the teacher know what question to ask in a given situation? Effective questioning takes a great deal of practice and reflection on the part of the teacher. Often, we need to analyze a student's response or question rather quickly and then respond with an appropriate question for the student to consider. The ability to do this grows with experience. What we learn from working with one group of students gives us more possibilities to consider the next time this mathematical topic comes up.

Effective questioning is important for several reasons. First, through your questions, you help students develop their ability to describe their own thinking processes in a step-by-step manner, which will improve their understanding; this skill is also key to many aspects of mathematics. Secondly, student answers provide you with insights into the students' thinking: the concepts they understand, what they misunderstand, what is still eluding them, and their grasp of terminology. Finally, you are modeling the kinds of questions that you would like students to begin posing for themselves. Students need to think of useful questions on their own -- both questions they ask themselves as they solve problems, or those they ask their teacher or classmates. Questions are vital to learning.

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