You and I both know that questioning is a crucial part of learning and I’ve never felt that more than when teaching early maths mastery. I’ve become increasingly conscious of the need to ask the right questions and to understand the progression of thinking and early reasoning in order to pose the right questions at the right time. This understanding helps me to plan both guided learning time to practise answering these critical questions as well as independent activities that generate opportunities to ask a few well-placed questions that move learning forward.
It was incredibly hard to pick just 5 from all of the great questions you could be asking – please don’t limit yourself! – but these are the ones that made the cut. Read on for my top 5 questions that you should be asking your early mathematicians. Enjoy!
1. What can you see?
Before children can start to reason and explain their maths, they need to be able to notice the maths in what they are looking at. Give children practice at noticing mathematical properties or concepts in mixed ability groups so that a wide range of ideas are shared and heard. For example, you could show the children a half dozen egg box with 4 eggs in – 3 yellow and 1 red – and ask them What do you see? Remember to set the expectation from early on that children answer verbally in full sentences, supporting those who need help with this. Here are some of the answers you could expect and that you could move children on to:
- I can see some eggs in a box.
- I can see 4 eggs in 1 box.
- I can see 3 yellow eggs and 1 red egg.
- I can see 3 eggs on the top and 1 egg on the bottom.
- I can see that the eggs are in a ‘r’ shape.
- I can see an even number of eggs.
- I can see two empty spaces in the egg box.
- I can see that there is room for 6 eggs in the box because there are 4 eggs in there and 2 eggs are missing.
2. What’s the same? What’s different?
Using what the children notice mathematically can be put to good use when matching, comparing, sorting and problem-solving. Coming in at #2 (and technically two questions!), What’s the same? and What’s different? should feature in your maths questioning to help children make connections, communicate their ideas clearly with good mathematical language and to promote reasoning. Check out the useful Same But Different Math site for ideas and a range of images that you can use in your classroom.
3. Why is this not…?
When children can recognise similarities and differences in the maths that they see, they can start to use what they know to generalise and apply their knowledge in a range of contexts. By asking them Why is this not…? you are practising retrieval from their long term memory and reinforcing connections. For example, you might show a picture of a square and ask Why is this not a triangle? or write the equation 4 + 2 and ask Why is this not 5?
4. Can you prove it?
Often a follow up question to #3, this is one of those annoying teacher questions that is, nevertheless, a good way to probe a student’s understanding and helps to clarify the knowledge in their own mind. It is a question that more able students can sometimes struggle with, as they will often say things like, I just know or my brain told me. All fine when the numbers are small or the concepts are simpler but when the maths becomes increasingly complex, this lack of clarity about how they knew the answer can lead to some shaky foundations to build upon. With modelling and practise, proving the answer becomes another skill they can draw upon that will pay dividends further down the line.
5. Is there another way? And another?
So, I’ve put 7 – 3 on the whiteboard and the children have pottered away to find the answer. They proudly (hopefully) tell me it’s 4. Can you prove it? I ask… Yes, Evie shows me 7 fingers, puts down 3 and shows me the 4 fingers left. Brilliant! Evie is using her fingers to bridge between the abstract calculation and practical equipment. However, not all of the children are this far along and also, some have gone beyond using their fingers. So, largely ignoring the answer to the question, I ask Is there another way? Yes, Alex knows that 5 and 2 make 7 so he took an extra 1 off the 5 because it was taking away 3 rather than 2. Amazing! Alex is flying high and understands how to use compensation to support mental calculation. However, Shia still looks a little confused, he needs to work with something practical (some follow up work is required there to help him keep up), and I can see Tia has drawn pictures on her whiteboard to help her, which is a strategy that hasn’t come up yet. So it’s time to ask And is there another way? A classroom with a culture that values the various routes to the answer as much as – if not more than – the answer itself is an important facet of maths mastery learning. Try it in your classroom and you’ll soon find you have more confident mathematicians who are excited to tell your ‘their way’ of working out the answer!
I honestly could write a 10 page blog on questioning for early maths mastery but, if you’ve stuck with me this long already, you’ll be relieved to hear I didn’t! Hopefully, these top 5 questions help to illustrate how an understanding of early maths progression can help you ask the right questions at the right time. If you need some more guidance with this, all of the Early Maths Mastery planning documents have comprehensive questioning included, matched to a range of activities and progressive, interleaved inputs. You can download a free sample here.
I’d love to hear what your top 5 questions are – what’s the same about our top 5 questions? What’s different? 😉 Let me know how you get on!