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# Students Learn by Answering the Mathematics Question and Teachers Learn From the Students’ Attempts

Good questions are particularly suitable for this because they have the potential to make children more aware of what they do know and what they do not know. That is, students can become aware of where their understanding is incomplete. The earlier question about area and perimeter showed that by thinking about area and perimeter together the student is made aware of the fact that the area can change even though the perimeter is fixed. The very act of trying to complete the question can help children gain a better understanding of the concepts involved. The manner in which some children went about answering the following question illustrates this point.

James and Linda measured the length of the basketball court. James said that it was 25 yardsticks long, and Linda said that it was 24 ½ yardsticks long. How could this happen?

Some fifth and sixth grade students were asked to discuss this question in groups. They suggested a variety of plausible explanations and were then asked to suggest what they need to think about when measuring length. Their list need to agree on levels of accuracy, agree on where to start and finish, and the importance of starting at the zero on the yardstick, avoid overlap at the ends of the yardsticks, avoid spaces between the yardsticks, measure the shortest distance in a straight line.

By answering the question the students established for themselves these essential aspects of measurement, and thus learned by doing the task.

As we have discussed, the way students respond to good questions can also show the teacher if they understand the concept and can give a clear indication of where further work is needed. If Linda’s teacher had not presented her with the good question she would have thought Linda totally understood the concepts of area and perimeter. In the above example, the teacher could see that the children did understand how to use an instrument to measure accurately. Thus we can see that good questions are useful as assessment tools, too.