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.
Several Acceptable Answers
Many of the questions teachers ask, especially during mathematics lessons, have only one correct answer. Such questions are perfectly acceptable, but there are many other questions that have more than one possible answer and teachers should make a point of asking these, too. Each of the good questions that we have already looked at has several possible answers. Because of this, these questions foster higher level thinking because they encourage students to develop their problem-solving expertise at the same time as they are acquiring mathematical skills.
There are different levels of sophistication at which individual students might respond. It is characteristic of such good questions that each student can make a valid response that reflects the extent of their understanding. Since correct answers can be given at a number of levels, such tasks are particularly appropriate for mixed ability classes. Students who respond quickly at a superficial level can be asked to look for alternative or more general solutions. Other students will recognize these alternatives and search for a general solution.
In this article, we have looked more closely at the three features that categorize good questions. We have seen that the quality of learning is related both to the tasks given to students and to the quality of questions the teacher asks. Students can learn mathematics better if they work on questions or tasks that require more than recall of information, and from which they can learn by the act of answering the question, and that allow for a range of possible answers.