The art of teaching is based on effective questioning strategies. Asking good questions is an informative process that needs development, refinement, and practice. Teaching through questioning is interactive and engages students by providing them with opportunities to share their thinking. The classroom should be an community of collaborative learners whose voices and ideas are valued.
In order to obtain more information from students during classroom discourse, we need to develop an open-ended questioning technique and use a more inquiring form of response, encouraging students to defend or explain both correct and incorrect responses. Here is an example of closed and open questioning for the same situation:
Closed—What unit should be used to measure this room? (limiting)
Open—How could we measure the length of this room? What choices of units do we have? Why would some units seem more appropriate than others? (probing—encourages students to think about several related ideas)
Good questioning involves responding to students in a manner that helps them think and lets you see what they are thinking. Response techniques involve:
According to NCTM's Professional Standards, the teacher of mathematics should orchestrate discourse by—
The Professional Standards propose five categories of questions that teachers should ask:
"Do you agree? Disagree?"
"Does anyone have the same answer but a different way to explain it?"
"Does that make sense?"
"What model shows that?"
"Does that always work?"
"How could we prove that?"
"What would happen if...?"
"What would happen if not...?"
"What pattern do you see?"
"Have we solved a problem that is similar to this one?"
"How does this relate to ...?"
Through modeling of investigative questioning, the teacher should help students learn to conjecture, invent, and solve problems.
Burns, M. (1992). About teaching mathematics: A K-8 resource. Sausalito, CA.: Marilyn Burns Education Associates.
Gridley, C. Robert (1992). Asking better classroom questions. Portland, ME: J. Weston Walch.
Lindquist, M. M. (1988) Assessing through questioning. Arithmetic Teacher, 35(5), 16-19.
National Council of Teachers of Mathematics: Commission on Teaching Standards for School Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.
Pandley, T. (1991). A sampler of mathematics assessment. Sacremento: California Department of Education.
Stenmark, J. K. (Ed.). (1991) Mathematics assessment: Myths, models, good questions, and practical suggestions. Reston, VA: National Council of Teachers of Mathematics.
Vermont Department of Education. (1991). Looking beyond "the answer:" The report of Vermont's mathematics portfolio assessment program. Montpelier, VT: Author.