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:

- Waiting. Time is a critical component. An immediate judgment of a response stops any further pondering or reflection on the part of the students.
- Requesting a rationale for answers and or solutions. Students will utimately accept this procedure as an expected norm.
- Eliciting alternative ideas and approaches.

According to NCTM's Professional Standards, the teacher of mathematics should orchestrate discourse by—

- posing questions and tasks that elicit, engage, and challenge each student's thinking;
- asking students to justify their ideas orally and in writing.

The Professional Standards propose five categories of questions that teachers should ask:

- Category 1 questions focus on helping students work together to make sense of mathematics.
"Do you agree? Disagree?"

"Does anyone have the same answer but a different way to explain it?"

- Category 2 contains questions that help students rely more on themselves to determine whether something is mathematically correct.
"Does that make sense?"

"What model shows that?"

- Category 3 questions seek to help students learn to reason mathematically.
"Does that always work?"

"How could we prove that?"

- Category 4 questions focus on helping students learn to conjecture, invent, and solve problems.
"What would happen if...?"

"What would happen if not...?"

"What pattern do you see?"

- Category 5 questions relate to helping students connect mathematics, its ideas, and its applications.
"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.

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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.