Wednesday, 15 June 2022

Mathematics is not a "building block" subject

I've been reading Alf Coles and Nathalie Sinclair's I Can't Do Maths! Why children say this and how to make a difference. It takes five ideas about teaching maths that they've identified as myths, and explains how the myth works, and what might be done about it.

I'd already seen Alf Cole's TEDx video about the first myth, that mathematics is a building block subject, where we build more complex ideas on top of simple ideas.

The situation of learning a language by being immersed in a complex whole is of course a really powerful instance of children learning within complexity. My English as an additional language learners learn - fast - by being immersed in the life of the class. They somehow pull out of the messy whole all the grammar and vocab that they need.

As Alf Coles says, Caleb Gattegno calls this using the 'powers of their minds', and asks why we can't make complex demands on those powers in teaching maths.

Alf Coles suggests that if you're not succeeding in mathematics class, instead of needing something simpler, perhaps you need something more complex.

This is the subject of the first chapter of the book: Myth A: Maths is a Building Block Subject. 

'The idea that in order to learn something, you need to start with the simplest ideas and slowly build upwards - constructing one block at a time - seems to be common sense. The primary maths curriculum in schools in most countries in the West is designed with the tree idea in mind.'


'...what if our image of learning and mathematics were more like a mangrove forest than a single structure or tree? Mangroves grow as a decentralised network, each part dependent on other parts, growing upward and downward and sideways too. If there is a problem, no need to go back to the starting point; no need to find the trunk or the ground floor, since there is no one thing upon which everything else depends.'

This does really seem to go against the usual assumptions about mathematics learning.

And yet I do see it in operation in my students.

In our learning in Early Years of course, where it is children's play that leads the way, we often see the mathematics embedded in something else - maybe in building a house together. Or some other kind of arranging with blocks. Or pretending to run a shop. Or making a pattern of squares. They present their learning to themselves not in the most simplified form but in a complex context in which much of the learning is hidden from easy observation.

Often the complex task is more satisfying than the simpler one - perhaps in some sense it is more efficient, though it looks much less orderly and logical to us.

Take that thing of arranging squares. Today I saw this.

I've written before about how compelling filling a space can be for young children. In terms of motivation, it seems to beat the kind of linear ABAB patterns we teach when we begin pattern. And yet, here we are dealing with a 2D space rather than a 1D space, with a lot more complexity. And yet it is how young students seem to prefer to create their patterns. 

I've written about how one of my young students (not the only one) likes to build his Numberblocks-inspired numbers out of Polydron, rather than taking the more obvious path of simply using connecting cubes.

I've written a lot about using Cuisenaire rods (example). The authors too see the power of looking at arithmetic algebraically rather than numerically, and in their chapter on practicalities they go into detail on this. How powerful it is to see that two things are equal so vividly, and to have an easy way of saying it. 
Two reds are equal to one pink. 2r=p. Five and six year olds can get a really solid understanding of what equality means. And multiplication becomes counting. Two reds. Just like two apples. This can be a very different route from the counting and number-dependent route children usually follow.

I think there's a lot to be said for this mangrove approach - and thanks to Alf Coles and Nathalie Sinclair for articulating it so well! I'm going to be pondering this a lot more.

Tuesday, 22 February 2022

Why play?

Here's a nice thing to do. Go down to the Med with your blow-up kayak. Push it out to sea, straight out to avoid the waves rocking it over, hop beaches, admire the mansions along the coast, take pictures, pull the kayak onto a beach and walk across the hot sand to a bar and sip cocktails together, looking out to sea.

All lovely. To do this, I also need to take my phone, to take pictures, and my card, to pay, and my glasses to see properly. It means we need to be quite careful with waves and water getting in the boat. This is the usual pattern, and it's a lot of fun.

But one time, I tried something different. I left my glasses, phone, and money with the people on the towels.

Oh, now there's nothing to get wet, I don't need to worry about water getting in the kayak. I can aim for the waves. I can deliberately capsize it, sit on the upside-down kayak, try, and succeed in, righting the kayak. 

This is play. I don't need to get from A to B without getting wet. I don't need to do the correct thing. In fact, I'm going to try out the incorrect thing. I'm going to take risks, try things to the limit. I will get wet, and it will be OK.

And I learn a lot from it, not that I was setting out to. I feel more connected with the kayak and with the sea. I know better what they can do together. I'm less afraid of what might happen. I know how the boat behaves in the waves at different angles. I know that if we get knocked over, I can sit on top of it, and we can right it. 

This play thing seems at right angles to the A to B functionality of the boat. It doesn't get me anywhere, it doesn't keep the boat the right way up, it doesn't keep me dry. And yet, my knowledge is now broader, more reliable, more comprehensive. 

That's what play does.

Saturday, 1 January 2022


Over the holidays I've been reading David Graeber and David Wengrow's The Dawn of Everything, A New History of Humanity.

It's a big book, full of fascinating  and momentous ideas about the dawn of civilisation. One of the big things it does is to question evolutionary ideas about a progression from hunter gatherer innocence in small groups evolving to agriculture, to cities, to states.

There were huge sites built by hunter gatherers. There were cities all around the world that don't seem to have had kings or queens, but ran their affairs through discussion and deliberation. There were cultures that valued freedom highly and went to great lengths to avoid having that freedom taken away.

In fact some of those cultures might have brought ideas of freedom to the fore for Europeans.

Father Lallemant, a Jesuit missionary to the Huron in the early 17th century, wrote about the Huron in these terms:
From the beginning of the earth to the coming of the French, the Savages have never known what it was so solemnly to forbid anything to their people, under any penalty, however slight. They are free people each of whom considers himself of as much consequence as the others; and they submit to their chiefs only in so far as it pleases them.
The Jesuits naturally found that this 'wicked liberty of the savages' made it harder for them to submit to their authority.

Published account of indigenous Americans and their not always favourable view of Europeans were popular reading in Europe. One such account, Louis Armand, Baron de Lahontan's Curious Dialogues with a Native of Good Sense who has Travelled, published in 1703, amounted to a critique of European life, from the point of view of the Huron chief, philosopher-statesman Kandiaronk.
Lahontan: This is why the wicked need to be punished and the good rewarded. Otherwise, murder robbery and defamation would spread everywhere, and, in a word, we would become the most miserable people upon the face of the earth.

Kandiaronk: For my own part, I find it hard to see how you could be much more miserable than you already are. What kind of human, what species of creature, must Europeans be, that they have to be forced to do good, and only refrain from evil because of fear of punishment? ...
Kandiaronk saw the Europeans as lacking in both freedom and equality. Graeber and Wengrow propose that views like this from outside Europe helped shape demands in Europe for 'Liberté, Egalité, Fraternité'.

Graeber and Wengrow refer to three primordial freedoms - freedoms that are often taken away when a sovereign emerges:
  • the freedom to move;
  • the freedom to disobey;
  • the freedom to create or transform social relationships.
Naturally, I think of education in terms of some of the themes of the book, freedom in particular. School can be an institution where all those freedoms are almost completely removed.

But - and I'm thinking of the kind of play-based setting that we work in with young children - they can also be places where those freedoms are valued.

I was struck by a tweet by Ben Mardell that shows some teacher documentation of some Pre-K students talking with their teacher:
Ricardo: What does freedom mean?

Ms Hannah: That's a good question Ricardo. I'm glad you asked that.

Children's responses -

- It means you can play!

- You can move around and run.

- You can finally stop what you HAVE to do.

- When someone comes to play and you say yes.

The book has made me see freedom more specifically, and also as a value that in various times and places, sometimes in complex societies, in cities even, has been guarded jealously. Some cultures went to great lengths to make sure they could travel and be welcomed elsewhere, and to avoid arbitrary power emerging. These things are well worth guarding with our youngest students.

And that last freedom - to create and transform social relationships... I would like to have more situations where the students genuinely, as a group as well as between pairs, have more opportunity to make the most of this freedom.

Monday, 20 December 2021

Building mathematics

 One of my students, A, has been with me for over a year now. He was just three years old when he started, and without much English. His favourite thing was to get the Playmobil cars out, fill them with people, and quietly act out stories with them on his own.

He did lots of other things too. Here he is in the playground, back then in September 2020, with two other students, making a house with the giant Polydron:

We've watched lots of Numberblocks (see my post on this), where numbers are represented by blocks.
I haven't asked anyone to do this - most of the things that happen in our pre-K (Early Years) classes are child-initiated and developed - but A has been spending a lot of time exploring numbers by building cuboids out of Polydron. While others were content to use our pre-existing interlocking cubes, A wanted to make the cubes himself from squares. He makes other things too, like this house with an interesting floor plan:
But here's 8 (called 'Octoblock' in Numberblocks), built by A from individual cubes:
There is a Numbrblocks episode called Terrible Twos, where 4 splits into two 2s who tickle the other numbers while they sleep which makes them split into ones. Here is A's version in magnetic Polydron, a 4 made of two 2s.
It even comes into his story writing, which is usually about T. rexes and triceratopses:
The building continues:
Recently he's developed an interest in writing. Here he is practicing writing the numbers:
Children also play with the Numicon and tell me equations. They've heard a lot of these on Numberblocks. Here's one from A:
What I really am pleased about is that all this learning is initiated by him (in a climate of appreciation and encouragement of course). It is very much his own and at his pace. I'm pleased that all the four year old students in my class have also found their own different ways to this, enjoying representing numbers and equations. A has also influenced younger students in the class too. T in particular is a real enthusiast for creating the same kind of Polydron 3D numberblocks.
As the students do, T told me some equations linked with what he was doing, and then told me a few more he knew:
I think it's from these landmarks that young students begin to build their number sense, so what he's doing seems just right to me.

Saturday, 20 November 2021

Where mathematics comes from

 At the moment I'm reading a little about materiality in learning - how physical materials and the physical environment and what they can do are a kind of teacher as we interact with them.

It made me think about how that is true for learning mathematics. In my last post, I pondered what young children are learning as they construct a play house out of bricks together and move into it.

One of my tentative conclusions is that in arranging matter, they are learning to arrange matters in the broadest sense of the word. They are learning what it is to try things out boldly and get results, what it is to work as a team.

In an older post, I thought about the natural powers that students bring into play when they do mathematics. 

This is from John Mason and Sue Johnston-Wildery:
The kinds of powers that are relevant for learning mathematics are ones that learners will have demonstrated by the time they arrive at school. Learners have innate ability to emphasise or stress some features and to ignore others, enabling them to discern similarity and difference in many subtle ways. They can also specialise by recognising particular instances of generalisations, and they can generalise from a few specific cases. In addition, they can imagine things and express what they imagine in words, actions or pictures, together with labels or symbols.

(my emphasis) 

A couple of things about both agency and these natural powers. First, we learn them by exercising them in the world, interacting with people and things, primarily through play. Secondly, they don't serve us only in mathematics, but in all disciplines and areas of life. 

That second point is important I think. The roots of mathematics are much much broader than the 'trunk' - stretching out into all areas of play and interaction. Squashing playdough, spinning round and round, having a conversation, singing a song, jumping in puddles, listening to a story. And not just because these things have elements of geometry, measure, arrangement and number in them, as they often do - but because all our growing powers are needed for the learning of any discipline.

I often return to this: 

Maryam Mirzakhani, the first - and only! - woman to win the Fields Medal, only got into mathematics near the end of her schooling:
"What are some of your earliest memories of mathematics?"
"As a kid, I dreamt of becoming a writer. My most exciting pastime was reading novels; in fact, I would read anything I could find. I never thought I would pursue mathematics until my last year in high school."

(from here

Could Maryam Mirzakhani's love of reading have supplied important ingredients that later went into her mathematical work? I think so.

The foundations of our mathematical learning are in all our learning. 

Maybe - and I'm blundering into unfamiliar territory here - this connects with that old chestnut: 'Is mathematics discovered or invented?'

The question often seems to be answered without thinking of individual development. As if mathematics were a free-standing thing that wasn't created and recreated each time an individual explores and learns about it.

I want to say that it is very much discovered - in our first steps and first reaching we encounter magnitude. It's in the world that we learn the agency, the natural powers and all the other building blocks of mathematical thinking. It's in how we arrange the bricks in that play house, how we create an inside and outside, how we space the toy cars on top. And in the logic of how one step leads to another. The material of the world is full of the different logics of mathematics. And when we abstract it away from its inception in the physical world, again and again we return to the world at further points - we have already felt the inflection points of a curve when cycling in figures of eight on the tricycle in the playground. We know what a plane is from the many floors we have moved across well before we meet the Cartesian plane. In algebra, we often get a whiff of the idea of magnitude that lies behind the cat's cradle of manipulations we do with symbols.

And of course mathematics is invented too. The directions we take are ours. They reflect our economies and social structures. Counting for buying and selling and taxes. Measuring for sowing seeds - and taxes. Another planet would have a very different body of mathematics.

As usual, my ideas around this are half-formed, rough-draft, and probably too briefly expressed. 

Practically, working with 3-4 year olds, I'm confident that all the story reading and writing, all the conversation, all the art work, messy play, construction, games, roleplay, sensory play, small world play - and of course play with mathematically structured materials and moments - is the best thing, not just for learning in general, but for the learning of mathematics too.

Wednesday, 27 October 2021

Arranging things

Three of my new students (aged 3 and 4) have been settling in this half term. They have been doing lots of playing alongside each other, but this was one of the first times they cooperated on a common project, building a house.

The conversation was in Spanish, so I couldn’t benefit from it. Once it was built, they had encircled themselves and they enjoyed being in the inside they had created and furnished it with sundry items to make it more of a home:

Our early years team have been working with Anne Van Dam, looking at what ‘working theories’ the children are developing in their play. This follows the work of Helen Hedges

“Working theories are present from childhood to adulthood. They represent the tentative, evolving ideas and understandings formulated by children (and adults) as they participate in the life of their families, communities and cultures and engage with others to think, ponder, wonder and make sense of the world in order to participate more effectively within it. Working theories are the result of cognitive inquiry, developed as children theorise about the world and their experiences. They are also the ongoing means of further cognitive development, because children are able to use their existing (albeit limited) understandings to create a framework for making sense of new experiences and ideas.” (Hedges & Jones, quoted here)

This concept of working theories builds on the work of Bruner, Claxton, Gopnik, and Vygotsky. It sees children as actively building their understanding through the thinking and play they do. I like it a lot for its respect of children's thinking, seeing the active way in which children make sense of their worlds.

And yet... there's something in the fit of this to the kind of loose parts play that doesn't feel quite right. I can't put my finger on it exactly...

If I were to list some of the ideas and understandings that children might be building in this activity, I might say:

  • 'I can make friends playing alongside other children'
  • 'I can get better at communicating by doing it'
  • ‘I can create a new space by enclosing it’
  • ‘I can align bricks and build them up to a wall’

  • ‘Here is a place that I belong’

  • ‘I can make this place into one I belong in even more’

  • ‘I can build’

  • ‘I can work together with others on a common goal’

  • ‘We can achieve things together, and it feels good’

  • ‘We can bring things into our space’

These are not once-for-all understandings that are achieved and then we move on, but ones that grow and grow through students’ time at school. That enclosing is a schema, ie a repeated behaviour, seems to indicate that the understanding that is built up doing it is something that needs to grow incrementally and be connected with lots of other thoughts and experiences.

The more experienced children in the class seem to have this understanding much more firmly, and to build and create together with so much more ease. 

But, like so much of children’s play, it doesn’t seem to be directly pursuing a question (like ‘Where do birds sleep?). Outwardly, it’s more directed towards making, production than it is to finding out. They are, ultimately, finding out, but the immediate impulse is one of creation. In this way the play seems to have more in common with the arts than with the sciences.

This is a thought that I’m still mulling over.

And now this sketchy diagram that I’ve drawn is making me think. The impulse to create, to make, to perform, to challenge oneself allows a feedback loop. It puts the results of our action (beige in the diagram) into the world as something that we can observe. A kind of design cycle. We are building up theories about the kinds of achievements we can have in the world.

Helen Hedges writes ‘Learning may appear somewhat disorganized, perhaps appear to move around and then return later to topics, questions and ideas, may call on invention and imagination to connect ideas…’

To me, most learning is disorganised, full of imagination and invention. So much of learning, of building theories, is devoted not to how the physical world works or even to social and cultural learning considered as learning what’s already there. A huge amount of learning seems devoted to managing possibility. I have these materials - what could I do with them? How might I deploy them, arrange them? I have this time with my friend? How might I fill it? I’ll learn to wildly invent, to put some unheard-of combination boldly into place - and I’ll see what happens then.

New Zealand’s Te Whāriki Early Childhood Curriculum has a section called Learning Dispositions and Working Theories. “Dispositions that can be useful for learning include playfulness, whakatoi (daring), persistence, resilience and imagination. Children also develop dispositions towards domain knowledge…”

What I’m trying to get a grip on doesn’t seem to simply reduce to dispositions though. It is a more disorganised-seeming, less direct way of obtaining knowledge about what daring and playfulness can achieve, what can be done with freedom and within necessity, how the social and physical environment can be remixed. It centres around agency, and uses whatever is at hand to achieve its undefined aims. It achieves its goal of developing capable and skillful being and making in the physical and social world, but its means are more indirect than what comes to mind when we think of theory-building: curiosity -> question -> search -> answers.

This simple house the children make seems to bring so many aspects of learning together. Mathematics is in there too. The straight line of the bricks, the way they are placed in the same orientation, and on top of each other to create layers. The way the lines of bricks are parallel to create the rectangular floor plan, and how the cars are arranged, spaced out evenly.

That word arrange. It means both to place things by some kind of design, and also, metaphorically I suppose, though we're no longer conscious of any metaphor, to organise anything in life. 

Maybe the play follows a similar path to the way the word has travelled? We play at organising loose parts, we learn, ultimately, to organise our lives, whatever the variables it gives us.

And now I'm curious what the roots of that word arrange are:

Ah - putting something in a ring. And there's the word rank, like ranks of soldiers.

It's always fascinating to see the proposed Proto-Indo-European root of a word, and all the offshoots of that:

I find this nexus of related words more than interesting. It's almost as if play recapitulates etymology. We encircle ourselves with loose parts, we line them up in ranks, and doing this we are researching, building working theories about our own agency, our abilities to work with others to build a home, our abilities to arrange matter and matters.

(Adapted from notes we each made for our work with Anne Van Dam)

Tuesday, 14 September 2021


In PK, we've been watching the first two series of Numberblocks. These present the numbers zero to ten as different characters who, by the normal rules of arithmetic portrayed dramatically, have the power to transform into one another.

If you're not familiar with Numberblocks, you could watch the first two minutes of this video. (You don't get full episodes on Youtube, you get composites of a number of episodes. We've watched Series 1 and 2 on DVD and on Netflix.)

What do I like so much about it?

Our young three to five-year old children like it so much, want to watch episodes again and again, go home and watch further episodes.

Numbers are represented as arrangement of cubes. All sorts of things become clear like this. Number as area. Addition as combining, subtraction as splitting. Odd and even-ness à la Numicon. Square numbers. Arrays of numbers. All sorts of interesting avenues for investigation are opened up. For instance in the clip above, the numbers are represented as different polyominoes, different arrangements of squares. What tetrominoes are possible? I'm a fan of figurate numbers, of area-as-number (have I talked to you about Cuisenaire?) because I find it gives children a powerful way into number and arithmetic.

Numbers as character and narrative. We all love a story, and the Numberblocks stories are well thought out and entertaining. They also work because of the mathematics. Again, in the Strampolines episode, the story is about what different arrangements are possible. 'One' is sad because she can only make one arrangement, but is cheered up when she learns that copies of herself make up every arrangement (polyomino factorisation anyone?). 

The animation and the music. Yes, we sing along to the songs!

The equations that emerge as numbers transform are represented flexibly. So we don't just see 4+1=5, we see 5=4+1, and also 5-1=4. Children get a sense of what equality means, and they also begin to see how equations relate to arithmetic before having to write them themselves. Often they want to write equations, and it's something we've built on to give the power that writing ones own ideas brings.

Students enjoy recreating and exploring what they watch. Here, for instance, a four-year old student observed that 25 is a square.
I pointed out that there seems to be one missing, and he had a good think about that:
One piece of evidence about how well it's worked for the students, is doing 'Number of the Day' with them on the first day of their next year in Kindergarten. I've been able to pop in and work with them on this. In the past, students have been a bit blank when we've asked them what they know about 1, or have commented on what its shape makes them think of, but this year there were equations.
By day eight, with a bit of help from Cuisenaire rods, the equations were really flowing.
And here are the day 9, here are lots of the ideas the Kindergarten students shared:
So, a big thank you to the Numberblocks team, and also to Debbie Morgan who has been their chief mathematical advisor.

Sunday, 1 August 2021

Sleeper effects

There are two studies I keep thinking about. Both involve large numbers of students. Both concern 'sleeper effects' - effects that don't appear straight away, but emerge later.


The first is a study in Boston Massachusetts, and I heard about it via Alison Gopnik. Public preschools had been made available to everyone, but there was such demand that places had to be decided by lottery. Effectively this produced a very large randomised trial, involving more than 4000 students.

The study, The Long-Term Effects of Universal Preschool in Boston, produced some very interesting results. Preschool attendance did not improve test scores in elementary school. It did however have a sleeper effect that emerged later in high school. More students who'd been to preschool finished high school, and more went on to college.

That's fascinating, isn't it? Four-year olds going to preschool didn't effect their test scores in the immediate years following, but it did have a significant positive effect much later. 

What would be your guess about how this works?


The second study was conducted with an even larger number of students, more than 12,000 this time. They are at the other end of their formal education, at a four-year college. Keith Devlin writes about it in this piece

Students are randomly assigned to different teachers, and their test results are collected over a long period of time. There are two really interesting results, and I'll just touch on one of them here.

As Devlin puts it:
But here is the first surprising result. Students of professors who as a group perform well in the initial mathematics course perform significantly worse in the (mandatory) follow-on related math, science, and engineering courses. For math and science courses, academic rank, teaching experience, and terminal degree status of professors are negatively correlated with contemporaneous student achievement, but positively related to follow-on course achievement. That is, students of less experienced instructors who do not possess terminal degrees perform better in the contemporaneous course being taught, but perform worse in the follow-on related courses.
We find that less experienced and less qualified professors produce students who perform significantly better in the contemporaneous course being taught, whereas more experienced and highly qualified professors produce students who perform better in the follow-on related curriculum.
Isn't that interesting! Students of more experienced and better qualified teachers get poorer test results that year - - - but better results in subsequent years!

What a fascinating sleeper effect! What would be your guess at an explanation for that?


Saturday, 31 July 2021


As an EY team we look back at 'Moments in the Day' together - times when something in the children's play and learning strikes us. We share documentation and discuss. In our last time doing this in the school year, Estelle shared this photo with us:

She wrote:
I’m still puzzled about this activity that S., G. and M. engage in regularly.

It is often initiated by M. but not always (I think). I’m not sure I’ve watched closely enough at the right moment. I wonder what skills they are using here and that makes me think that I almost need to try it myself to find out. Perhaps they will allow me to quietly join in…. Otherwise I could have a conversation with them.

There is definitely a quality to this play that is ‘safe’, mindful and we can assume that it is good for their well-being based on the repetition. Maybe for the artist no. 1 there is a feeling of being the leader, being ‘seen’ and valued. For artist no. 2 perhaps the feeling of making a connection in this way has meaning.

Perhaps I can join in and see what is happening; it all happens so fast.
I've noticed children doing things in unison a lot too, and I'm interested. What do we derive from this? 

As teachers, we think of our jobs as being about building individual creativity, individual agency, so where does this leading and following, this doing (almost) the same thing fit in?

Questions like this are quite hard to get a handle on. We have hunches, but they don't feel like the complete story.

Perhaps we should take up Estelle's suggestion and just draw the same thing together, and see what it feels like 'from the inside'. There's no guarantee that we'll feel the same as the students do of course, but it might help.

What else does copying look like in our classes?

Here's some more examples.

At a certain count, friends are jumping off chairs in unison:

Pairs of students making the same as - or here, the reflection of - each other's designs with the square tiles in trays:
We're at the pattern block table and a student says. 'Simon, let's play I make something and you copy it.
Using large foam pattern blocks to make rockets together:
Painting together:
So what's going on?

I can't say, but there are certain things I sense might be going on. This passage from Sloman and Fernback's The Knowledge Illusion might help orient us:

Sharing attention is a crucial step on the road to being a full collaborator in a group sharing cognitive labor, in a community of knowledge. Once we can share attention, we can do something even more impressive—we can share common ground. We know some things that we know others know, and we know that they know that we know (and of course we know that they know that we know that they know, etc.). The knowledge is not just distributed; it is shared. Once knowledge is shared in this way, we can share intentionality; we can jointly pursue a common goal. A basic human talent is to share intentions with others so that we accomplish things collaboratively.

Let's make a list of some of the things happening: 
  • Feeling comfortable with each other,
  • Feeling comfortable with an activity,
  • Being in the same space with each other,
  • Somehow having an idea of doing things in unison,
  • Understanding the proposal,
  • Accepting the idea together, sharing the intention, having a joint project,
  • One  leading, other(s) following (how flexible is this?),
  • Monitoring each other's actions,
  • Recreating each other's creation,
  • Comparing the results,
  • Completing the project.
That's part of what happens, and it's a lot. But there's also the significance. What does it mean to do the same thing together? 

That time the children synchronised themselves jumping off the chairs, was such a moment of joy. It seemed like a celebration of friendship and of feeling great in their bodies, in the classroom and together! Not all the examples are so exuberant, but there's a pleasure and significance in not just being in the same place and time, but in the same self-chosen project.

As an adult, I can appreciate this too. In fact, teaching together with the PK team, we plan our activities together. We then, mostly, work in our separate places. But there's a tremendous affirmation in having the same understandings and objectives, in approving of the same resources, environment, activities. And, of course, bringing our stories of what happened back to each other. Our work together is so intertwined that what we do with our students isn't usually the idea of any one of us, it's a kind of team thing.
Then there's singing Beatles songs with friends. We're not exactly doing the same thing: one of us plays piano, another guitar, another ukulele, but mostly we sing the same melody and words. What is it that's so satisfying about it? There's something in there about the whole being more than the sum of the parts.

In our 'Moments' meeting, Nick mentioned that humans succeeded where Neanderthals didn’t because they shared ideas; they didn’t have bigger brains, it was just that they shared their ideas.This is part of what it is to be human, and what has given us our success.
I first came across this idea in Rutger Bregman's great book Humankind. Bregman has this chart:
Following anthropologist Joseph Henrich's modeling, Bregman invites us to think of a planet with two tribes. One tribe, the Geniuses, are great at inventing things, but not so good at sharing their ideas; the other, the Copycats are not such great inventors, but do share. The Geniuses are a hundred times better at inventing. The Copycats on the other hand are ten times better at sharing. Which tribe do inventions spread through most?

The Copycats. 

So, I'm coming round to valuing these times when children get into total synch with each other.

And next year, I'm going to copy Estelle's idea, and try to catch more of what is happening as children copy each other.