“Good learning starts with questions, not answers.” Guy Claxton, Professor in Education and Director of CLIO Development, University of Bristol. Questioning is a great way for teachers to check your primary pupils’ understanding of specific KS2 Maths concepts while also allowing children to actively participate in their own learning of important ideas. A well thought out questioning strategy in primary Maths can also help to build the relationship between teacher and pupil by encouraging engagement and improving verbal fluency of key Maths concepts. It’s a win-win!
This blog post will guide you through the 9 key questions that will have the most impact on your teaching and your primary pupils’ learning at Key Stage 2 whether you’re preparing for National Assessments or just building depth in their understanding of Maths.
1. Are you sure?
Developing pupils’ metacognition is crucial if we want them to be less reliant on the teacher as the person who ‘knows’. If a pupil is used to asking a teacher ‘Is this right?’ and getting a response then they are likely to not have checked their answer, not gained a deep enough understanding of the concept they are learning or have their need for affirmation so ingrained over years of schooling that they simply have to ask.
Asking ‘Are you sure?’ with a questioning tone will instantly flip the tables and create blind panic amongst your whole class. Especially when you ask the question as often when they are right as wrong. Even more so if you follow it up with ‘Well okay, if you are sure…’ or ‘If it makes sense to you…’
Now, obviously blind panic is not what we are aiming for, but it is a stage they will need to briefly enter until they get used to this and the other questions in the post. Soon they will pick up the idea that they really have to know if they are right or not and crucially, why. This leads us into a key follow-up question…
2. How do you know?
To be able to answer ‘Are you sure?’ confidently, pupils will have needed to have checked their calculation/explanation themselves, more and more often before they have even given their initial response. Asking ‘How do you know?’ ensures this by asking them to share their reasoning with you, a group or the whole class.
The result of this increased metacognition is children will be more reliant on themselves (and each other) for checking their understanding, method and answer.
3. What do you notice?
Alongside metacognition, developing pupils’ ability to generalise can reap huge rewards. In other words, encouraging pupils to be mindful and look for patterns within and outside the mathematical area currently being learnt. This also helps their number sense. Asking pupils ‘What do you notice?’when showing 2 calculations or problems at the same time can help children to see what is similar and different. It’s a key question when building procedural variation. It also uncovers where a pupil’s understanding is, showing whether their current line of thinking is relevant to the current learning, in turn enabling you to nudge them towards more relevant thinking where necessary.
For example, displaying 47-8 and 47-6 may yield answers such as ‘8 and 6 are both even’ which are not particularly relevant, ‘the 4 and the 6 can be added to make 10’ shows up misconceptions and ‘you don’t have enough ones (7) to subtract 8 but you do with 7-6’ which shows pupils are making relevant connections, assuming the concept being learnt is exchanging. From here it is a small step to ask for generalisations about subtracting ones from ones that can be applied whenever faced with that situation. I.E. ‘You must always exchange when you try and subtract more ones than you have.’
4. What’s the same and what’s different?
If you want a question that serves the same purpose as ‘What do you notice?’ but is more confining in its responses, asking ‘What’s the same and what’s different about these 2 calculations/problems/statements?’ will push that conversation on with you still guiding the direction.
5. Can you convince me?
This is another question that can help develop generalisation. Asking individuals or small groups to work together to convince you of something develops their depth of understanding and ability to reason. Here are some examples:
‘Convince me that subtraction is the opposite of addition’
‘Convince me that all multiples of 8 are multiples of 2’
Flipping around the previous question’s example, ‘convince me that you always need to exchange when you subtract a 2 digit number (subtrahend) where the ones are greater than the initial number (minuend)’
6. Is there another way?
‘Is there another way to find 25% of £80?’
‘Is there another way to work out 47+28?’
‘Is there another way you could have used to find all the possibilities?’
Use these 25 word based problem solving questions, complete with bar models to practice bar modelling with your KS2 class
These kinds of questions help children who have not used a modeled or shared method realise they are not ‘wrong’ because theirs is different (they may be less or more efficient). It will also highlight to children that in Mathematics, as in life, there are many ways to skin a cat. It can also be used as a general challenge activity for pupils.
7. Is it always, sometimes, or never true?
This is a great question to further develop children’s ability to generalise and, dependent on the question, their number sense. As with all the questions, it develops reasoning skills and can deepen understanding.
For example, ‘Is it always, sometimes or never true that you should round and adjust when you subtract 9 from a number?’
8. Can you imagine?
Building pupils ability to visualise things without actually doing it themselves helps in a number of disciplines such as Computing or Science as well as Mathematics. Looking specifically at Mathematics, it helps pupils understand problems and raises their ability to reason with greater understanding.
So in a word problem, if you ask a pupil to imagine the train pulling up at that station at that time and then continuing on its journey to the next station, it can help contextualise an abstract time problem. It is also a handy way to nudge children away from requiring concrete apparatus when you think they are ready, for example, ‘Can you imagine exchanging that ten for ten ones?’
9. I think I understand what you mean, are you saying?
Okay, so our final question is not really a question. But it is in the same ball-park. You will always find times where a pupil’s ability to verbalise their reasoning is not quite at the same stage as their actual thinking and thought process.
Dependent on the situation and the pupil, you may find it supports them, your discussion or the pace of the lesson in general by saying ‘I think I understand what you mean, are you saying you would always round and adjust because you know that 9 will always be next to 10 so you will always be able to do the same adjustment afterwards?’
In other words, build on their reasoning, making it sharper or more concise so that the group or whole class can develop their understanding and the pupil giving the explanation can internalise their understanding further.
There are several variations on this question, such as ‘You’ve really tried hard to explain that… are you saying…’ or ‘It’s a really difficult thing to explain, you’ve helped me understand it I think. Is this what you mean…’
Preparation for KS2 Maths SATs
So there you have it. Almost 9 questions that when used across school will significantly impact on teaching and learning and ultimately, enable pupils to achieve with the National Curriculum, SATs and in using Mathematics in their general lives. There may still be gaps which exist in some of your pupils’ learning, which require further attention. You may find they need to be asked the right questions to get them talking mathematically. Many of the 5,000 pupils we work with every week love the fact that they have their own personal Maths tutor who they can talk, talk, and talk some more to. Many of our schools report a massive increase in their pupils’ verbal fluency in Maths and beyond.
If you think your pupils could benefit from the power of 1-to-1 Maths tuition and increased verbal fluency, let us show you how we can help your school raise attainment and build confident learners.