Teachers can learn a great deal about their students' level of conceptual understanding and reasoning skills by monitoring small
group and whole class discussion. The teacher who knows what to ask and when to listen can gather useful evidence about students'
understanding, and can use that evidence to determine next steps in teaching. Consider the teacher's role in the whole class discussion
described below, from a combined fifth and sixth grade classroom. The students are investigating the fractional relationships among
cubes and rods of different size. Their explanations refer to the relationship among two cubes, where five of the small cubes fit
along one side of the large cube.
In this brief episode, the correct answer surfaces right away, and then the discussion veers off to an incorrect answer.
How would you handle this situation? Would you bring the group immediately back to the correct answer, or would you allow exploration
of the incorrect answer as well?
What is David thinking? What is his strategy for counting cubes? What are some errors he has made? Has he reasoned correctly
in any ways?
What questions might you ask David to promote better understanding of volume in this context?
What questions might you ask Juan to help get his strategy and answer back into the discussion?
Do you think that other students can benefit from listening to this discussion? How so?
The National Council of Teachers
of Mathematics is a public voice of mathematics education, providing
vision, leadership, and professional development to support teachers
in ensuring mathematics learning of the highest quality for all
students. The views expressed or implied, unless otherwise noted,
should not be interpreted as official positions of the Council.