For years, I’ve wondered at how as a kid I found the monkey bars in a playground (often a jungle gym in the US) so much easier to swing on than I do as an adult. And I see our kids swinging around easily on them, while now it’s hard for me just to hang off them. The reason why is partly to do with the square-cube law.

The square-cube law is the deceptively simple observation that as you scale up dimensions — say, as you get taller — then area of the object increases proportional to the square of the length, while volume increases proportional to the cube of length. This fundamental relationship has enormous significance in the sizes and shapes of animals and the limits of how big trees can get and how big we can build our bridges and buildings.

Because the strength of our bones, muscles or wooden beams is proportional to their cross-sectional area, this means that while the strength of a larger object, assuming the same proportions as the smaller one, increases according to the square of a length, the weight (from the volume it takes up) increases according to the cube of a length. So, relative strength decreases as size increases.

Some corollaries are therefore that children’s small size relative to the area of their muscles and bones makes them relatively stronger than adults and so they can more easily support their weight as they swing on the monkey bars. In the same way, press ups are harder for bigger people than they are for smaller. And while an ant has tiny spindly legs, those legs could easily support 50 other ants of its size, whereas for an elephant to support its own weight it needs chunky legs — not spindly ones — and there’s no chance it could get close to carrying 50 other elephants on its back.

It’s also part of the reason short trees can be spindly, but big sequoias have relatively chunkier trunks, and we need increasingly strong materials to build bigger and bigger skyscrapers compared to the shed in your garden.

Galileo discussed this back in 1638, and it still requires some getting your head around today.

For this and other fascinating insights of scaling check out Scale, by Geoffrey West.

The Square-Cube law

I love Reggio Emilia’s concept of the environment as the third teacher. This idea works just as well in early childhood education as it does in a primary school classroom—or even an office. A thoughtfully designed environment can support learning, foster good habits, and boost overall wellbeing.

• The first teacher is the parent or classroom teacher.

• The second teacher is the student’s peers.

• The third teacher is the learning environment itself.

A well-designed classroom can act as the third teacher, shaping behaviour, sparking curiosity, and encouraging exploration.

I once had a mentor who said he could tell how a project was going just by observing the state of the project room—proof that our environments influence more than we realise.

What Makes a Classroom a “Third Teacher”?

To create a classroom that truly acts as a third teacher, consider these key elements:

Intentional Layout: Arrange furniture and materials to encourage collaboration, independent learning, and creativity. Open, uncluttered spaces can inspire curiosity and reduce overwhelm.

Visibility and Accessibility: Keep tools, books, and resources at children's eye level. This will help them feel a sense of ownership over their learning.

Natural Elements: Incorporate light, plants, and natural materials. Studies show these elements can improve focus, reduce stress, and create a warm atmosphere.

Documentation: Display students’ work on walls to celebrate progress and reinforce learning. This practice, central to Reggio Emilia, makes learning visible and creates pride.

Zones for Exploration: Create different areas for reading, experimenting, building, or relaxing. Giving children clear zones encourages diverse learning experiences.

Tips for Teachers to Maximise the “Third Teacher”

Observe and Adapt: Watch how students interact with the environment. Are they using spaces as intended? What sparks their interest? Adjust based on their behaviour.

Involve Students: Let children help design the space by suggesting ideas or creating artwork. This builds a sense of belonging and ownership.

Simplify and Rotate Materials: Too much clutter can overwhelm students. Keep materials fresh by rotating resources and ensuring every item has a purpose.

Focus on Flow: Think about how students move through the room. Avoid bottlenecks or cramped spaces, and make sure there’s room for both quiet reflection and active collaboration.

Technology as an Extension: In today’s digital world, some aspects of the “environment” live online. Design digital learning spaces with the same care as physical ones—easy navigation, engaging visuals, and clarity of purpose.

Too often today, our “environments” are hidden in software. Whether you’re designing a physical classroom, an early childhood learning space, or a workspace, consider how your environment could become a third teacher and how you could make the most of it.

This sketch features in my book Big Ideas Little Pictures

I originally made an animated third teacher version

The Environment as the Third Teacher in Early Childhood and Beyond

Winnie the Pooh teaches us how to speak plainly and avoid Owl Speak.

There’s a surprising amount of wisdom in A. A. Milne’s classic stories of Winnie-the-Pooh. If you haven’t read them for a long time, you could do much worse than try them again.

As one small example, I find there’s a lot of Owl Speak around as we get older, where we could all probably benefit from a dose of Pooh’s simplicity. Owl Speak includes never using a short, simple word when a long and complicated one would do. For example, in one revealing exchange, Owl explains:

“Well, the customary procedure in such cases is as follows.”

“What does Crustimoney Proseedcake mean?” said Pooh.

…”It means, the Thing to Do.” says Owl.

We learn more and more Owl Speak the more time we spend in school, only to have to work to remove it when we are older.

All the Winnie-the-Pooh books are lovely to read: Winnie-the-Pooh, The House at Pooh Corner, When we Were Very Young, and Now we are Six. Both quotes are from The House at Pooh Corner. Or, if you prefer to have the wisdom called out, you could try The Tao of Pooh, by Benjamin Hoff.

This sketch was updated for my book Big Ideas Little Pictures

How to speak plainly, by Pooh Bear

Beaches are amazing for play. Every time we go to a beach, I think, if you were to try and design the perfect toy, it would have many of the remarkable attributes of a beach - particularly the self-tidying feature. At some point, I should stop thinking that and just enjoy the beach.

If you like beaches too, you might enjoy the podcast episode fun at the beach where we talked about just what makes beaches amazing.

Beaches: amazing for play

This is my own observation — no rigorous research to reference. But, looking at our 2 year old as he’s transitioned from a baby, I’ve been led to think about our times on, say, public transport. A baby will largely only focus on what’s right in front of their faces or directly impinging on their senses. As they grow, the vicinity becomes their circle. So if you’re on the tube, anything within sight in the carriage is fair game for them to fiddle with or want to investigate. But adults are capable of just sitting there - thinking, about things far away, in the future or in the past. It strikes me that small children just can’t do that — life is what’s around them or nothing. Hence endless fidgeting and investigation. Brilliant.

The expanding circle of attention

4 Insights from Unconditional Parenting by Alfie Kohn.

Punishments and rewards are 2 sides of the same coin — and both are unproductive.

Love is not a scarce commodity that must be rationed.

Childhood is not a race

I learned this simple insight from The Baby Whisperer.

Children sketches