Designing and asking good questions
There are many different types of questions: closed, open, probing, curious, provocative, leading, clarifying, recall, divergent, convergent, reflective and inferential are just some we can think of right now. You may think of more. Each of these question types have a different purpose. How and when you ask can be as important as what you ask. So how do we go about intentionally designing questions that help promote mathematical thinking, knowledge and skill development in children of all ages?
In this section we will describe a range of strategies, with examples of possible responses and ideas to get you started. While it is difficult to predict what a child of any age will say in their responses, keeping in mind our current focus on early childhood we have tried to suggest examples that young children might say. We have also provided actual responses where possible.
So, what are we waiting for?
What do you notice?
What do you wonder?
Take a look at this beautiful photo of iconic Australian beach boxes. What do you notice? What do you wonder?
We asked some young children and this is what they said.
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What do you notice about these boxes?
- they look like little houses
- they are on a beach
- it looks like houses in a street
- they have steps that go up from the sand
- one is red and yellow stripes that go up and down
- one has a star on the front with little stars on the top
- this looks like a red and white star (union jack)
- one has a small pink door
- this one has stripes too, a green and pink one but they go this way (horizontal) not up and down
- they all look the same, not colours I mean, but the same
- they are made of wood
- they have bumpy roofs.
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What do you wonder about these boxes?
- who lives in them?
- who made them?
- why are they on the sand?
- where are all the people?
- where are the boxes?
- are there more?
- why are they different colours?
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These boxes are on Brighton Beach in Port Phillip Bay, Victoria. There are 82 boxes sitting in one row on this beach. 100 years ago, just like today, they provided privacy for families going for a day trip to the beach.
They also provide a wonderful context to start some mathematical conversations.
Building on these noticings and wonderings
Notice and wonder questions are open-ended. There is not one right answer. These kinds of questions allow us to probe children's previous knowledge and experiences, and find out the extent to which they connect these with the given context.
You might choose this picture intentionally, relating it to experiences children have mentioned, an excursion you have just been on, or because children are showing interest in the beach.
You may also choose to it with the intention of promoting mathematical thinking, taking the opportunity to listen for the kinds of mathematical language children are using, or trying to use, when explaining their observations and ideas about these boxes during notice and wonder moments. This intentionality would extend to helping the children use the appropriate mathematical language, infusing it into your conversation and activity. This kind of scaffolding is essential if children are to communicate their mathematical thinking.
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The children looking at the provocation picture of the beach huts have noticed many aspects that are non-mathematical, i.e. the colour, the sand and that they look like a house.
They have also noticed many aspects of these houses that provide potential for a mathematical exploration of language and concepts related to:
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different types of lines: parallel - coloured stripes or wood planks; intersecting - union jack,
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direction of the lines: horizontal and vertical - coloured stripes and wood planks
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2D shapes: stars on Australian flag, rectangles, triangles, corners
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3D objects: box-like objects (rectangular prism)
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volume: how much space does the whole box take up (may present us "how big is it"?)
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internal volume/capacity: how much does the box (as the container) hold?
Such concepts can be explored from the early years, as evidenced by indicators with a mathematical focus in the EYLF2.0 (AGDE, 2022). The older the children, the more potential there is to combine these concepts. For example, the relationship between 2D and 3D, and 3D objects and their volume.
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Moving from closed to open
The Notice and Wonder questioning approach can be used to promote the mathematical processes of noticing, observing, sorting, classifying, ordering, comparing, organising, identifying, naming, recording, communicating, predicting, explaining, discussing, reasoning, generalising, representing, and modelling promoted in the Early Years Learning Framework 2.0 (AGDE, 2023).
So, what next?
How can we design other open ended questions that promote a range of mathematical processes and opportunities.
How do we open that door?
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Designing open ended questions
Let's look at a strategy for opening up closed questions. Closed questions generally have one answer (usually the "right" answer), providing little opportunity for insight into children's conceptions and alternate conceptions (things they don't quite understand yet).
Sullivan and Lilburn (2004) suggest a strategy for adapting the questions we already use. For example, taking a closed or standard question then adapting it to make it a "good question" (p. 6).
In essence, we are reworking the original question to add modifiers like might, could, can you, and tell me which open them up.
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For example:
Closed question: What is a square?
Open Question: How many things can you tell me about a square?
You can see here that we have bolded the words that ask for many options, and italised a prompt that modifies the "what is" to a "can you tell me?".
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Closed question: Draw a shape with four sides.
Open question: I drew a shape with four sides, what might my shape look like?
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Notice that the first question provides you with an idea of whether children know what a 'side' is and whether they can draw 4 straight ones that join to make a closed shape.
In the open question, you will get a greater range of 4-sided shapes as you ask 'what might'. Some of the shapes children produce may look like your shape (make sure you have this ready to show), others will look different. Some might not be 4-sided shapes at all as the sides are not straight.
It is this range that provides you with the opportunity to discuss what a 'side' is and how we name and categorise 4-sided shapes.
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Closed question: Can you find a box that looks like the bathing boxes?
Open Question: How many different objects can you find that look like the bathing box?
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The closed question could invite a yes or no answer.
The open question assumes that there will be objects that look like the box (or rectangular prism) in the environment around them. It may be that you have a box like a tissue box, or a lego structure that looks like the bathing boxes, and use this as a stimulus for the search. As you know, it is helpful for children to have something to touch and manipulate when they are building their understanding.
The objects children bring back to the group can then be compared to the one you have shown.
This is a opportunity to conduct some comparing and contrasting conversations with another open ended question:
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What is the same about the objects we have found?
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What is different?
This naturally leads to sorting and classifying tasks, and the introduction of mathematical language that allows students to describe the attributes of their objects, i.e. flat, round and curved. With older children you may distinguish between faces (flat surfaces with straight edges) and curved surfaces.
"People don't like to tell you things but they love to contradict" - Sherlock Holmes
This is a great quote. And it provides food for thought in terms of provocative questioning.
Putting mathematical lenses on with this approach, and sticking to our Brighton bathing boxes theme, we could say some like:
I showed my friend this picture of the beach huts because because I love all the different colours.
She said what about the shapes?
I said there weren't any shapes, just huts.
Was I right?
Children who can see shapes will love to correct you.
This is an opportunity to ask:
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how do you know?
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what other shapes can you see?
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can we keep a record of the shapes we can see? (opportunity to record them)
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can you draw and decorate a bathing box with the shapes we have found?
We have been intentional here in creating a provocation that promote conversation about 2D shapes.
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If we move our focus to 3D objects, I could say:
I really like these boxes I saw on the beach but I think it would be too hard to make them.
What do you think?
Children will love to tell you they can make the boxes.
This is an opportunity to ask:
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if we use our blocks, which ones will we need and how do we put them together?
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instead of using blocks, is there a way we can make them ourselves?
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what will we have to think about (the flat faces, how many faces) when we are making the box?
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if we use playdough, how can we make the walls of the box flat?
Once again, we have been intentional here in provoking ideas about how we can create a rectangular prism, and/or a rectangular prism with a triangular prism as its roof.​
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Designing good questions is not always easy. We have found that it takes planning and practice. In our experience, writing down questions you might ask to promote mathematical thinking before you start small group conversations is beneficial. We acknowledge that different questions serve different purposes. We offer the above techniques to promote learning opportunities that promote and refine childrens' mathematical language and reasoning skills.
References
Sullivan, Peter, 1948- & Lilburn, Pat. (2004). Open-ended maths activities : using "good" questions to enhance learning in mathematics. Oxford University Press.