When I think about teaching mathematics in the early years, my impulse is to overthink it - and I suspect I'm not alone. I often jump straight to planning counting, number or shape activities.
Yet some of the most meaningful mathematical learning I see as a childminder happens when children are simply playing, exploring, reasoning and solving problems for themselves.
Spatial reasoning is a powerful example of this. It emerges through children’s play, both indoors and outdoors. One recent example came from Aaliyah's play, which provided me with the opportunity to support and extend her spatial reasoning.
Discovering spatial reasoning
Not so long ago, if someone had asked me to name the key mathematical areas for young children, spatial reasoning wouldn't have been at the top of my list. However, after completing a recent mathematics training course, I stopped to observe children more closely and realised just how much mathematical thinking is involved.
Spatial reasoning in maths is a child's ability to understand, visualise and manipulate how objects relate to one another in space. It plays a huge part in children's everyday experiences and supports the development of important foundations for later mathematical learning.
You can find out more by reading the Supporting children to make comparisons and connections approach in the Early Mathematics theme on the EEF’s Early Years Evidence Store.
Balancing (or not) on the beam
Recently, I observed three-year-old Aaliyah as she approached the beam.
As soon as Aaliyah stepped onto the beam, I noticed that she stretched her arms out to either side. It was something she did naturally and without hesitation to help her balance.
It got me thinking: Does she know why she’s doing this?
I asked, ‘Why are you stretching your arms out, Aaliyah?’
Aaliyah looked at me as if I had asked a very strange question and couldn't really give me an answer.
I suggested, ‘Let's see what happens if you keep your hands by your sides.’
The result was immediate - Aaliyah lost her balance, tumbled off and burst into giggles.
Aaliyah: ‘I can't do it, it doesn't work.’
I laughed along and said, ‘No, you can’t balance with your arms by your sides, can you?’
Aaliyah: ‘No, I need my arms stretched out so that I don’t fall off … like this.’ She showed me.
What I loved about this moment was that Aaliyah’s play turned into a genuine problem-solving opportunity. As I interacted with her, I thought mathematically - this enabled me to help Aaliyah explore and learn something new about balancing.
Aaliyah tested out and refined her new ideas: she wanted to know for sure if stretching her arms out really made a difference. I stepped back and observed. She occasionally looked to me for reassurance or guidance. Instead of telling her what to do, I encouraged her to keep trying and work it out for herself. She walked across the beam again and again - sometimes trying to keep her hands by her sides, seeing if she could make it work. When she lost her balance, she adjusted something. Sometimes she slowed down. Sometimes she changed where she placed her feet. Sometimes she moved her body differently.
Aaliyah was developing a greater understanding of spatial reasoning through trial and error. Every time she crossed the beam, she made a mathematical decision - she was thinking and playing mathematically.
Educators as mathematical thinkers
This vignette shows how my confidence and approach to mathematics has changed over time. I was able to see the maths in Aaliyah’s play and help her to develop it. Aaliyah’s maths learning came out of what she was interested in: it was led by her.
Children are often developing their mathematical understanding in ways that might not immediately look like maths. They are measuring, comparing, estimating, balancing, positioning and problem-solving through their play. I think sometimes, in our busy settings, we can miss valuable learning opportunities like these.
The thing that made a significant difference to Aaliyah’s learning is that I was present as a mathematical thinker. Had I not been, I would most likely have missed the opportunity to further her knowledge and understanding of balance.
Having made an intervention that helped extend her thinking, I stepped back, observed, encouraged her, and gave her time to explore further and consolidate her mathematical reasoning.
Moving children’s mathematical thinking on
Aaliyah’s story is a powerful reminder that mathematics is all around us: it is so much more than counting and number work.
Aaliyah certainly didn’t need me to ‘overthink’ a maths activity for her - she provided it for me!
Questions for reflection
- Can you make a short list of everyday activity that involves on spatial reasoning?
- Now can you think about how you could further a particular child’s understanding using one or two of these examples.
Want to know more?
The DREME network (Development and Research in Early Mathematics Education) Spatial Reasoning: Why Math Talk is About More Than Numbers
EEF Early Years Evidence Store: Early Mathematics