Good questioning techniques have long being regarded as a fundamental tool of effective teachers. Unfortunately, research shows that 93% of teacher questions are "lower order" knowledge based questions focusing on recall of facts (Daines, 1986). Clearly this is not the right type of questioning to stimulate the mathematical thinking that can arise from engagement in open problems and investigations.
Many Primary teachers have already developed considerable skill in good questioning in curriculum areas such as Literacy and History and social studies, but do not transfer these skills to Mathematics. Teachers' instincts often tell them that they should use investigational mathematics more often in their teaching, but are sometimes disappointed with the outcomes when they try it. There are two common reasons for this. One is that the children are inexperienced in this approach and find it difficult to accept responsibility for the decision making required and need a lot of practise to develop organised or systematic approaches. The other reason is that the teachers have yet to develop a questioning style that guides, supports and stimulates the children without removing the responsibility for problem‐solving process from the children.
Four Main Categories of Questions (Badham, 1994)
Starter questions
Questions to stimulate mathematical thinking
Assessment questions
Final discussion questions
1.Starter questions
These questions can guide the children through investigations while stimulating their mathematical and critical thinking. Teachers can gather information about their students' knowledge, reasoning and strategies.
How could you sort these.......?
How many ways can you find to ....... ?
What happens when we ......... ?
What can be made from....?
How many different ....... can be found?
2. Questions to stimulate mathematical thinking
These questions assist children to focus on particular strategies and help them to see patterns and relationships. This aids the formation of a strong conceptual network. The questions can serve as a prompt when children become 'stuck'. (Teachers are often tempted to turn these questions into instructions, which is far less likely to stimulate thinking and removes responsibility for the investigation from the child).
What is the same?
What is different?
Can you group these ....... in some way?
Can you see a pattern?
How can this pattern help you find an answer?
What do think comes next? Why?
Is there a way to record what you've found that might help us see more patterns?
What would happen if....?
3. Assessment questions
Questions such as these ask children to explain what they are doing or how they arrived at a solution. They allow the teacher to see how the children are thinking, what they understand and what level they are operating at. Obviously they are best asked after the children have had time to make progress with the problem, to record some findings and perhaps achieved at least one solution.
What have you discovered?
How did you find that out?
Why do you think that?
What made you decide to do it that way?
4. Final discussion questions
These questions draw together the efforts of the class and prompt sharing and comparison of strategies and solutions. This is a vital phase in the mathematical thinking processes. It provides further opportunity for reflection and realisation of mathematical ideas and relationships. It encourages children to evaluate their work.
Who has the same answer/ pattern/ grouping as this?
Who has a different solution?
Are everybody's results the same?
Why/why not?
Have we found all the possibilities?
How do we know?
Have you thought of another way this could be done?
Do you think we have found the best solution?
References
Badham, V. (1994) What's the Question?. Pamphlet 23. Primary Association for Mathematics (Australia)
Badham, V. (1996). Developing Mathematical Thinking Through Investigations. PAMphlet 31. Primary Association for Mathematics (Australia)
Bloom, B. (1956). Taxonomy of Educational Objectives Handbook 1: Cognitive Domain. New York: David Mackay
Dains, D. (1986). Are Teachers Asking the Right Questions? Education 1, 4 p. 368-374.
Sanders, N. (1966). Classroom Questions: What Kind? New York: Harper and Row.
Comentários