Physical activity and maths learning with young children

Here’s what the evidence tells us, with particular attention to the 3-4-year-olds age group and sex differences.


The Big Picture: Movement is Not a Distraction from Maths — It Is Maths

The idea that children need to sit still to learn is one of the most persistent — and harmful — myths in education. Research consistently shows that children who are more physically active demonstrate better attention, stronger working memory, faster processing speed, and higher academic achievement than sedentary peers.

https://www.personhood360.com/physical-activity-supports-learning-early-years/

The mechanisms are neurological: physical activity increases blood flow to the brain, stimulates the release of neurotransmitters (dopamine, serotonin, norepinephrine) that support mood, motivation, and attention, promotes neurogenesis in the hippocampus (critical for memory and learning), and strengthens the cerebellum — involved not only in movement but also in attention, language processing, and cognitive function. https://www.personhood360.com/physical-activity-supports-learning-early-years/


What Sedentary Behaviour Does to 3 – 4 -Year – Olds

Sedentary behaviour is associated with higher adiposity and poorer psychosocial health and cognitive development in children aged 0–4 years. https://pmc.ncbi.nlm.nih.gov/articles/PMC5575514/

Prolonged periods of sedentary time in early childhood are associated with an increased risk of depression in older children and adolescents. Anthropologists note something specific: reduced postural activity (standing and movement play) in early childhood reduces the ability to learn from experiences and produces developmental delays.

This has a direct implication for classroom design: we should evaluate how much time children are spending in sedentary positions and consider whether chairs are needed at every learning station. https://www.teachearlyyears.com/learning-and-development/view/physical-activity-early-years


Physical Activity → Numeracy: The Research Evidence

A large Norwegian study of 711 preschool children (mean age 4.6, 52% boys) found clear links between activity levels and numeracy. Associations with numeracy were negative for time spent sedentary and positive for time spent in moderate to vigorous intensities. Associations with numeracy were stronger in boys (R² = 5.58%) and older children (R² = 7.27%). https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.842271/full

Active mathematics lessons delivered daily across one month resulted in higher counting and number identification skills in young children. https://link.springer.com/article/10.1007/s10643-023-01532-5

The chain linking movement to maths runs through executive function — particularly working memory, inhibition and cognitive flexibility. Measurements of executive function in preschool predict achievement on mathematics and literacy in kindergarten. Working memory ability correlates with maths and reading scores among children aged 5–6. https://pmc.ncbi.nlm.nih.gov/articles/PMC4874515/


The Boy-Specific Finding: Particularly Important

Boys benefit more from movement-integrated learning than girls. Researchers speculate that boys — who show poorer self-regulation but higher physical activity levels than girls — may inherently need more movement, and that this stimulus more strongly and positively affects self-regulation in boys than in girls. This is consistent with the finding that physically active learning in school-aged boys benefits them more than girls. https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.842271/full

A controlled intervention study with 816 children aged 3–4 found that sex was a significant moderator for effects on early learning. Positive trends were found for boys while negative trends were evident for girls, as girls prefer more social, verbal, and less intensive indoor play and may find more intensive movement activity detracting from other activities that benefit them. https://www.tandfonline.com/doi/full/10.1080/02640414.2025.2460886

Research on embodied cognition found a parallel result: when movement was meaningfully related to a cognitive task (embodied condition), younger children profited more than older ones — and boys profited more than girls. https://link.springer.com/article/10.1007/s41465-018-0081-4

Physical play in the classroom was also found to be positively related to emotional competence, particularly peer relationships, in boys. https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2021.729272/full


The Critical Design Distinction: Embodied vs. Generic Exercise

Not all movement is equal. Research distinguishes between:

  • Generic vigorous activity before learning (useful for priming attention)
  • Embodied maths activity — where the body enacts the mathematical concept

There exists a substantial body of research evidence that embodied learning modes can enhance children’s mathematics learning, yet implementation of the research findings in classrooms has so far been limited. https://www.mdpi.com/2227-7102/14/7/696

Embodiment across mathematical domains can benefit mathematical learning, likely by providing an additional representation of the mathematical concept to strengthen encoding, by reducing cognitive load, and by inspiring the use of strategies and modes of thinking that non-embodied approaches don’t evoke. https://link.springer.com/article/10.1186/s41235-017-0053-8

A preschool intervention study found that embodied activities engaged the teacher and children in creating mathematical representations through body movements, and revealed connections between embodied activities and children’s development of subitising, counting skills, mathematical drawing, and number magnitude knowledge. https://www.mdpi.com/2227-7102/15/9/1170

Children who gestured while explaining maths problems were 50% more likely to transfer learning to new problems. https://www.structural-learning.com/post/embodied-cognition


Practical Nuances and Caveats

  • Intensity matters. Short bouts (~10 minutes) of vigorous “huff and puff” intensity activities can support children’s attention and self-regulation, so vigorous movement before a quieter maths task works well — but the learning itself should also integrate movement wherever possible.
  • Not all sedentary time is equal. Some quieter, focused sedentary activities (social play, drawing, narrative) do support self-regulation in girls specifically — so a blanket “movement = good, sitting = bad” framing is too simple.
  • The evidence base is still maturing. A large Norwegian longitudinal study of 3–4 year olds found no overall longitudinal associations between 24-hour movement behaviours and change in numeracy, though interesting gender-differential patterns emerged — a reminder that causality is harder to establish than correlation at this age.
  • Motor skills are the bridge. Direct and indirect associations have been found between physical activity, fundamental motor skills, executive functions, and early numeracy in preschoolers — meaning developing gross and fine motor skills through maths activities is likely doubly beneficial.
  • https://link.springer.com/article/10.1007/s10643-023-01532-5
  • https://link.springer.com/article/10.1186/s12889-025-24605-z
  • https://www.tandfonline.com/doi/full/10.1080/17461391.2022.2092777

There’s genuinely interesting counter-evidence worth surfacing. Here’s a critical and balanced look at what pushes back against the above summary.


Counter-Evidence and Complicating Findings

1. The Biggest Direct Challenge: A Large RCT Found No Effect on Maths

The most methodologically rigorous counter-evidence comes from the ACTNOW trial — a large cluster-randomised controlled study specifically designed to test what the earlier research predicted. A study of 816 children aged 3–4 years measured self-regulation, inhibition, cognitive flexibility, working memory, vocabulary, and early mathematical skills at baseline and at 7- and 18-month follow-ups. Results showed no effect of the physical activity intervention on cognitive or learning outcomes in the primary analyses. This is a significant finding because the study had high statistical power, used accelerometry to measure actual activity change, and was specifically targeted at the 3–4 age group that the previous research most often studied. https://www.tandfonline.com/doi/full/10.1080/02640414.2025.2460886

2. Effect Sizes Are Small and the Evidence Is Inconsistent

Even the meta-analyses that do find positive results are modest. A systematic review and meta-analysis of 29 studies involving over 11,000 children found positive overall effects of physical activity on mathematics in only 13 studies (45%), with neutral effects in 15 studies (52%). The overall effect size was small (ES = 0.23). In other words, more than half of properly controlled studies found no significant maths benefit from adding physical activity. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6873534/

A separate 9-month physical activity intervention also found that varied improvements in cognitive skills were observed for different variables in both intervention and control groups, with no robust evidence for physical activity intervention-related improvements specifically. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7557372/

3. Sedentary Time and Inhibition: An Unexpected Positive Link

One of the Norwegian preschool studies uncovered something that directly complicates the “more movement = better maths” story. Associations with inhibition were positive for time spent sedentary — meaning more sedentary time was linked to better inhibitory control. This association with inhibition was stronger in girls (R² = 3.12%). Inhibitory control is itself a strong predictor of mathematical performance, which means for some children, particularly girls, some quiet, focused time may be supporting the very self-regulatory skills that underpin maths learning. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9037291/

4. The Dual-Task Problem: Moving and Learning Simultaneously May Not Work Well

There is a legitimate cognitive concern about asking young children to move and learn maths at the same time. Researchers have flagged that young children may be susceptible to interference during learning and consolidation when performing physical activity concurrently with academic instruction. When one study directly compared active and sedentary maths lessons on what was actually learned, children in physically active and sedentary lessons showed similar learning and retention of quantity estimation — the main difference was improved attention and reduced off-task behaviour, not superior maths acquisition. https://www.sciencedirect.com/science/article/abs/pii/S2211949321000028

5. Not All Sedentary Activity Is Equal — Quiet Cognitive Play Matters Too

The framing of “sedentary = bad” is challenged when researchers distinguish between types of sitting. Simply reducing sedentary time without incorporating stimulating activities may fall short of promoting cognitive improvements — a meta-analysis found that while increased physical activity was consistently linked to better cognitive performance, interventions focusing solely on reducing sedentary behaviour were less effective. https://pmc.ncbi.nlm.nih.gov/articles/PMC11755889/

Crucially, sedentary activities that are cognitively demanding — puzzles, drawing, construction play, book-sharing — appear to have distinct value. Active screen-based sedentary behaviour (e.g. computer use) tended to enhance cognitive functions in boys at age 5–7, while passive sedentary behaviour (e.g. TV viewing) had more negative cognitive impacts on girls. This suggests the quality of sitting matters as much as the fact of sitting. https://www.sciencedirect.com/science/article/abs/pii/S1755296625000171

6. Free and Quiet Play Builds the Self-Regulation That Supports Maths

A longitudinal study found that increases in academic time and structured activities employed to boost preschoolers’ school readiness and academic achievement at the expense of play time may ultimately hinder their academic performance — declines in play time during the preschool years may negatively impact self-regulation, which in turn could harm academic skills. https://pmc.ncbi.nlm.nih.gov/articles/PMC10688615/

And this extends to quiet, unstructured play specifically: the more time preschoolers spent in free choice activities, the greater their gains in inhibitory control — a key maths precursor. This free play includes sedentary forms like construction play and small-group activities, not just physical movement. https://www.sciencedirect.com/science/article/pii/S0885200621001411

7. The Boy Advantage from Movement May Be Overstated

While the previous summary highlighted that boys benefit more from movement-integrated learning, the evidence is nuanced. Girls showed a small negative effect from the physical activity intervention at 18 months — and this isn’t simply that movement helps boys more, but that an intervention optimised for movement may displace other activities (social, verbal, quieter play) that are more beneficial for girls’ development, artificially inflating the apparent boy advantage. https://www.tandfonline.com/doi/full/10.1080/02640414.2025.2460886


The Synthesised Picture

Taken together, the counter-evidence points to three important refinements:

  • Movement is not a sufficient condition for maths gains — it depends heavily on whether the movement is conceptually tied to the maths content, not just vigorous activity happening near maths.
  • Causality is unclear: children who are naturally more physically active may already have better executive function for other reasons, and the correlational studies can’t separate this.
  • Sedentary cognitive engagement has its own value — particularly for inhibitory control and focused attention, which are equally important maths precursors. For game design, the quality of cognitive demand during still play may matter as much as whether children are physically active.

Can we teach children to solve simultaneous equations by deduction, in their first term of Reception?

I spoke at MathsConf14 about how simultaneous equations are not as difficult as we make them out. In fact, if we teach them with manipulatives and pictures they are child’s play. This made me wonder about how young a child’s play is it? If we can get very young children to deduce the value of 2 or more unknowns then couldn’t we use these same methods with much older pupils to help them get it?

In the past, I have succeeded in getting pupils at the end of Reception solving pictorial simultaneous equations by deduction (not trial and improvement) and Year 1 pupils solving simultaneous equations with cups by deduction. I wondered at how young an age might it be possible to get pupils to solve the cups version by deduction.

Because this involves working with pupils in the first term of Reception, it has to be done as fun and magic with the magic cups and the magic counters, and each session is just a few minutes with tiny steps taken in each one. Pupils are invited to play with me but always have the option not to or to opt out as soon as they don’t want any more. It is usually the case when I play a game with Nursery and Reception pupils that I stop a game before they want to.

Checking the prerequisites

My initial interactions were to check that key prerequisites were in place before moving onto the games:

  • Number names (they know the number names in the right order)
  • Rational counting (they count objects giving each one the correct number name)
  • Cardinality (they know that the last name in the count represents the quantity)
  • Conservation (once they have counted or subitize 5, the quantity remains 5)
  • Subitizing to 5 (they can tell by looking how many without rational counting)
  • Well-developed part-part-whole concept
  • Number bonds for 5 (they know the pairs of numbers that together make 5)
  • Hierarchical inclusion (they know that in 5 objects we can find 5,4,3,2,1, and 0 but not 6)

Because we build the development of these into our Nursery activities, environment and play, the pupils I am working with already have all of these in place at the start of Reception.

Game 1

‘When you close your eyes, I will hide the 5 counters under the Blue cup and the Red Cup. There will be a different number of counters under the cups because they are different colours. Close your eyes’. I hide the counters. ‘Now open your eyes. Do you know how many of the 5 counters are under the Red cup? This means you really know how many there are under the Red cup, not just a guess’.

blog 1p1

If they reply that they do know, for example they say they know there are 4, then we have a look to see. It takes some pupils a few goes getting it wrong to begin to understand the difference between ‘knowing’ and ‘thinking/guessing’. If they say a number more than 5 then we have to work at that as well. For some, their first answer is ‘No’ because they realise straight away that it is not possible to know how many there are.

When they say ‘No’ then we discuss what might be under the Red cup and the Blue cup – number bonds for 5, preferably given in a systematic list (this is an example of an equation with 2 unknowns so that we cannot give the solution, but because they are whole numbers, we can list the possible solutions). I then show them how many there are under the Blue cup and ask them if they now know how many there are under the Red cup (this has now become an equation with only 1 unknown and so we can solve it). If their number bonds for 5 are strong then the answer is pretty much instant; they also tend to model their answer with fingers because they are used to showing their answer like this. They are not counting on their fingers to work out the answer – the answer is coming from long term memory – it is their non-verbal way of communicating their response.

 

To Be Continued as we attempt to move towards trying to solve the following type of problem by deduction not trial and improvement or guess and check. This will involve tiny steps and we may well run into problems with ‘cause and effect’!

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Friday 14th September 2018

I couldn’t find time to visit our EYFS block this week until today. My 4-year-old collaborators from last week were in a TGIF frame of mind today and understandably wanted to run around outside – who can blame them!!

I did, however, manage to recruit a couple of other Reception playmates and one of them was able to play/solve Game 1 and also managed Game 2 – this is where I expected to hit a stumbling block, but he got it. In fact, he went from never having done any of this to solving Games  1 and 2 in a matter of minutes!

I found out that I need to change the way I ask one of the questions because I failed to take into account the literal way in which they interpreted a question I asked them. Me:’Where did these 2 extra counters come from?’ Pupil: ‘From the bag’ (on the table).

Game 2

Attempt 1

Me: ‘Here are the Blue and Red cups and they have a total of 5 counters hidden under them. Do you know how many under the Red cup?’

blog2p1

Pupil: ‘No’

We discussed that he could not know because he could not see and could only have a guess from 0 to 5.

Me: ‘I will now bring in another Red cup and it has exactly the same number of counters hidden under it as this first Red cup, (adds an extra 2 counters to the original 5) and now there are 1,2,3,4,5,6,7 counters here. Do you know how many counters are hidden under this new Red cup?’

blog2 p2

Pupil, after some thinking time: ‘No’

Attempt 2

I remove the extra 2 counters and the new Red cup.

Me: ‘I will now bring in another Red cup and it has exactly the same number of counters hidden under it as this first Red cup, (adds an extra 2 counters – yellow side up- to the original 5) and now there are an extra 2 counters here. Do you know how many counters are hidden under this new Red cup?’

blog p3

Pupil, after some thinking time: ‘Two’

Me: (moving those 2 counters alongside the new Red cup) ‘So there are 2 counters under this Red cup. How many under this (original) Red cup?’

blog p4

Pupil: (instantly) ‘Two’

Me: (moving  2 counters alongside the original Red cup) ‘So how many counters must be under this Blue cup?’

blog 2 p5

Pupil: (instantly) ‘Three’

I then reveal each cup in turn to show that he is correct.

Reflection:

I learnt from doing this with Year 1 pupils, in the past, that it is the ’cause and effect’ that is the issue here. I have to get them to realize that the cause of the extra 2 counters is the introduction of the second Red cup, and so they may then deduce that there must be 2 counters hidden under it. If, for example, you get them to close their eyes whilst you bring in the extra cup and counters and then ask them to open them, then they do not tend to make that link – they have to see it happening. The long-term aim is for them to compare the two situations, see what is the same and what is different and hence deduce the number of counters under the extra cup – this will enable them to deduce the counters under all the cups.

It was interesting to see the different responses to when I counted the new total of 7 and when I highlighted the extra 2.

This gives me hope that the aim may well be achievable. This pupil has managed most of the key steps in a matter of minutes and my target is the end of the autumn term, doing only about 5 minutes a week with them.

 

Friday 21st September 2018

Game 3

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NB There is no movement when presented like this, just two static lines – a pair of equations with 2 unknowns and 2 given facts.

This was completed today by ‘Pupil 3’ today in a 5 minute session. I prompted with questions:

  • How many in the Blue Cup and Red cup altogether? (Row 1)  [5]
  • How many in the Blue Cup and 2 Red Cups altogether? (Row 2) [counted 7]
  • How many more in these cups than in these cups? (Compare Row 2 with Row 1) [2]
  • How many in the Red Cup (Row 2)? [2: He moved 2 of the counters alongside the Red cup] How many in the other Red cup (Row 2)? [2: He moved 2 counters alongside the other Red cup]
  • So how many in the Blue Cup (Row 2) [3: He moved the remaining 3 counters alongside the Blue cup]
  • So how many in Blue Cup (Row 1)? [2 then corrected to 3]
  • So how many in Red Cup  (Row 1)? [2]

Whenever he gave me the correct number of counters hidden under a cup, we looked to see if he was correct – except for the one error when I asked him again.

Looking ahead

Another Pupil 4 is just behind this stage and I hope to complete this with him next week. I am hoping that Pupil 3 will do much of this with less prompting next week.

  • Pupil 3 had 5 minutes last week and about 5 minutes today with no practice in between.
  • Pupil 4 had about 3 minutes last week and about 5 minutes today with no practice in between.
  • I have several others in the pipeline to get going with in the next week or so if I can find the time and also, hopefully,  catch up with Pupils 1 and 2 again.

 

I may attempt to get parental permission to film these sessions (faces not shown) so that I can share this with you – much more powerful to witness rather than read about it.

 

13 November 2018

I have managed to find time at last to get back to this today. I now have 4 pupils solving these equations with cups and counters and 2 more pupils ‘working towards’.

An interesting point was raised on Twitter today and I would like to clarify my position. I am totally opposed to ‘too much too soon’ in EYFS and do not believe that Reception children should be doing simultaneous equations – I made this clear in my vlog with Craig Barton. What I do want to demonstrate is that if we use manipulatives and a visual approach to finding the value of unknowns then it makes it much easier than if we teach solely through procedures. As with much of my approach to teaching, I believe that if we introduce topics to older children with the CPA approach that we use with younger children then both teachers and pupils may find it less of a struggle than they currently might do. It is looking like the sort of deduction required to solve for two unknowns is literally child’s play for some (but not all) young children and I think that there are some lessons to be learnt for teaching with these ideas when working with much-older pupils.