Prepare questions in advance

Questions to find out what students know

These questions can be used to check whether the student understands the task. They also help the student attend to the information they have access to – information provided within the task or from their prior knowledge or experience.

• What is this question asking us to find out?
• What information do we have?
• What can you see?
• Are there any parts of the task that are unclear?
• What do you know already that could help you with this problem?
• How could you use something that you already know to help you solve this problem?

Questions that provide guidance or hints

Questions can be used to help students make connections and form generalisations. They can also be used to help a student who is stuck find a way forward.

• Have you seen a problem like this before?
• What strategies did you use?
• What do you know that can help you here?
• How does this task relate to the skills we practised at the start of the lesson?
• Can you see a pattern?
• Can you draw the problem?
• Is there a faster way to work it out?
• Are there any special words (or numbers) in this problem that we should be noticing?
• What size answer would you expect to get?

Questions to help a student explain their reasoning

Understanding a student’s logic (sound or flawed) is the starting point for determining the learning experiences the student needs in order to move forward. For this to happen, the student’s thinking needs to be visible. The following questions help a teacher to hear what is happening in a student’s mind.

• How did you do that?
• How did you work it out?
• What did you say to yourself?
• Can you show me with this equipment or with a drawing?

Questions that require a student to defend their ideas

The small-group setting of an ALiM group is an ideal place for students to participate in mathematical discourse by justifying their ideas in a non-threatening environment.

• Can you give me an example?
• Will that always work?
• How do you know you’re right?
• What would happen if …
• Use these counters to show me that your method works.

Questions to help a student consider alternative strategies

It’s important for students to understand that there may be several ways to approach a problem. This should not devalue the strategies they have employed but rather should encourage them to explore other possibilities or to listen attentively to the ideas of their peers. This shifts the focus from “the answer” to the process used.

• Is that the only way to get the answer?
• Did anybody else do it that way?
• Can you solve the problem in another way?
• Is there a faster way to find out?

Questions that position the teacher as co-learner

When working in a small group or with an individual, the teacher can act as a problem solver, who suggests ideas and responds to the suggestions of the students.

• I wonder what will happen if …
• What strategy could we use to check this?
• Will it work if we do it like this?
• Can I use the same method to work this one out?
• I’m going to test it out. Let me know if I’m getting something wrong.

Questions to help a student reflect

Reflection plays an important role in consolidating learning. A teacher can ask questions to identify whether students recognise the key concepts or strategies the session has been based on. Ideas can then be recorded, for example, by displaying different strategies on the classroom wall or by including them in a learning journal.

• What important ideas did we explore today?
• What were some different ways that we solved a problem?
• What have you learned that you could apply to other problems?
• Have you heard an idea today that was important or useful?

Using statements to promote dialogue

Statements can be more useful than questions in promoting dialogue between students. After you have used the questioning techniques outlined, students should be ready to engage in mathematical discussion among themselves. Try introducing some teacher statements along with questions to promote discussion between students:

• That’s interesting … tell us how you approached the problem.
• So you’re saying …
• Another example would help us understand your working better.

Back to Resource 6: Building understanding through effective questioning and modelling