​From procedures to concepts
One of the core concepts that young children have to learn in mathematics is commutativity: understanding that 1+2 means the same as 2+1 (or a+b=b+a). Counting begins as a process in time, the process of ‘counting on’. Taking two fingers and adding one finger on to make three fingers is not the same process  as taking one finger and adding two fingers on to make three fingers. To understand that these two processes are the same implies taking a perspective that is able to see at least two different time-based processes together at once.  

The time perspective from which cummutativity makes sense is different from and larger than, the  time perspective of 'counting on'. Moving from doing addition as procedural 'counting on' to understanding the concept of cummutativity is a change that occurs within time. But more than just being a change within time it is also a movement into time. 

Vygtoksy specifies that what he means by system is based upon on the model of mathematics. He even uses the example of cummutativity to illustrate a general feature of conceptual thought that he calls ‘the law of equivalence’, writing ‘Thus, the number one can be expressed as 1,000,000 minus 999,999 or, more generally, as the difference between any two adjacent numbers. It can also be expressed as any number divided by itself or in an infinite number of other ways’. His claim is that this capacity to be represented in different ways within a conceptual system is what distinguishes true concepts from children’s spontaneous ideas. 

Children begin with temporal and contextual experience, understanding addition only as counting forwards on the fingers of your hand for example, and they end up with a more abstract and general understanding such as that  a+b=b+a regardless of context or of time. One implication of what Vygotsky is claiming about conceptual thought, following Spinoza, is that the role of the teacher is to help children move from experiencing things within time to understanding their meaning outside of time.
​

Expanding time
 
Spinoza was probably wrong, or at least misleading, in his claim that there is a perspective outside of time - the point of view of eternity. The fact is that we can only see things from within time and within contexts. That is just how thought works. But if he was wrong, he was wrong in an illuminating kind of a way that can help us to understand what education is really all about. The idea that we might one day see things ‘sub specie aeternitatis’ occurs to Spinoza only because there is a direction of travel in education from being trapped within a narrow time perspective to having a bigger time perspective - an expanding time perspective from which we can look back and compare different moments of time with each other in order to make meaning out of our experience. That there can be a movement into time as well as a movement in time is the essence of education. This simple idea is summed up by the well known quotation: ‘Those who cannot remember the past are condemned to repeat it’ (Santayana 1905). 
 
One way to re-interpret Vygotsky's ZPD is not that the teacher leads the child from a perspective within time to a perspective outside of time but that the teacher leads the child from seeing things only within one time context, that of the physical present, to being able to see the same things also from the point of view of other time contexts. Science does not provide us with timeless truths – no more than does religion or art - science is an ongoing fallible dialogue about the truth of things, a dialogue between real people in real contexts. However, the time and the space of the cultural dialogue of science is very different from the time and space of talk in a classroom. The time-space of the dialogue of science extends over thousands of years and is global in reach. The role of the science teacher in the classroom is to weave together the very large time-space perspective of science with the smaller and narrower time-space perspective of a face to face dialogue with a child in a classroom. It is one thing to observe a feather and a metal ball fall at the same rate in a vacuum chamber (in a You Tube video perhaps); it is quite another thing to derive from this an understanding of the concept of gravity. Knowledge arises in science as the answer to questions that are asked within a dialogue. For a child to acquire conceptual understanding they need first to be a participant in the long-term dialogue of science. This means to link the time-space of the classroom to the time-space of Gallileo dropping different objects from the leaning tower of Pisa and also to link this to the time-space of current experiments in the CERN collider that might determine our future understanding of gravity (https://home.cern/news/news/experiments/new-antimatter-gravity-experiments-begin-cern).

​Figure 4: ‘Jacobs Ladder’. The Padua Baptistery, 14th century, Giusto de Menabuoi

A two-way ladder
Vygotsky sometimes seems to present education as a one way ladder leading the child away from false ‘participatory’ concepts embedded in time and replacing these with a true understanding derived from a conceptual system that is essentially atemporal or outside of time. The great danger of formal education on this one-way model, a danger articulated by Paulo Freire, Ivan Illich and many others, is that it can disempower children by removing their truth – the truth of their experience in the present moment – and replacing it with someone else's truth, a truth which leaves them feeling inadequate and unhappy. Recent concern about the mental health consequences of pressuring children to do well in examinations perhaps illustrates what can go wrong with a one-way view of education (https://www.theguardian.com/society/2018/dec/27/exam-stress-creating-troubled-generation-ex-civil-service-chief-gus-odonnell). But the ideal of education as a journey into time is about children finding more meaning in their present moments and not less. Michael Oakeshott, for example, wrote of education as giving children their birthright inheritance of culture so that they could become more fully human . Without education, for Oakeshott, we are just like animals, physical bodies trapped in physical time and space - with education we become cultural beings participating in an shared cultural time and space, the unbounded time and space context that Oakeshott referred to as ‘the conversation of mankind’, a continuing conversation that he claimed began in 'the primeval rainforests' (http://www.rupertwegerif.name/blog/oakeshott-on-education-as-conversation).
 
I like the story of Jacob’s ladder  (Figure 4) because it describes angels not only going up the ladder from Earth to Heaven but also angels coming down from Heaven to Earth. At times Vygotsky mistakenly seems to suggest that education is about replacing understanding that arises from full-hearted  participation in the present moment with understanding conceptualised in a very dry rationalist sort of way as locating (subsuming) events within an abstract logical system. But at other times he presents the Zone of Proximal Development as a genuine two-way dialogue in which the teacher has to take on the child's perspective in order to engage with it and so to draw the child into participation in the long-term dialogue of culture. 

​Education does not need to be about taking meaning away from the present moment. It is not just about angels going up to Heaven. It can be and ought to be just as much about the angels coming down the ladder from Heaven to inform the present moment with greater  meaning. Bakhtin, for many the key philosopher of dialogism, used the term ‘chronotope’ for the inextricable combination of space and time in experience. He described how the chronotope (time-space) of readers was brought into a dialogic relationship with the chronotope (time-space) of texts. A dialogic relationship is a two way relationship in which there can be mutual understanding arising from an inter-illumination of perspectives. Bakhtin’s ideal of education is of a journey from  the chronotope of ‘Small Time’, the short-term everyday concerns in which we 'fuss about', as he put it, to what he called ‘Great Time’, the unbounded dialogic space in which all cultures and all times are able to communicate together. This vision of education as a journey into time is not about leaving behind our participation in the present moment - it is about expanding and deepening that participation. Bakhtin, for example, described how his appreciation of his own times, the time of the Russian revolution and its aftermath, was enhanced and enriched through his reading of texts from ancient Greece (Bakhtin 2010, introduction).

The teacher's role in education is not to replace one timescale with another, the living present of a child's experience with the dead eternal ‘truth’ of a formula or a text-book. It is to weave together two different time-scales, the short-term time-scale of a face to face dialogue in a classroom with the much longer term time-scale of the dialogue of humanity - or what Oakeshott called 'the conversation of mankind'. As in the picture of Jacob's ladder, the angels of education travel both ways. The angels climbing up refresh the long term dialogues of culture with renewed participation, whilst the angels climbing down enrich and expand the present moment, providing the insight and the wisdom that comes from experiencing everything in the light of larger perspectives and longer timescales.

Bibliography

Bakhtin, M. M. (2010). Speech genres and other late essays. University of Texas Press.

De Spinoza, B. (2001). Ethics. Wordsworth Editions.

Freire, P. (2018). Pedagogy of the oppressed. Bloomsbury Publishing USA.

Guardian (2018) Exam stress creating 'troubled generation', says ex-civil service chief. (https://www.theguardian.com/society/2018/dec/27/exam-stress-creating-troubled-generation-ex-civil-service-chief-gus-odonnell)

Illich, I. (1973). Deschooling society (p. 46). Harmondsworth, Middlesex.

Lemke, J. L. (2000). Across the scales of time: Artifacts, activities, and meanings in ecosocial systems. Mind, culture, and activity, 7(4), 273-290.

​Mercer, N. (2008). The seeds of time: Why classroom dialogue needs a temporal analysis. The Journal of the Learning Sciences, 17(1), 33-59.

Oakeshott, M., & Fuller, T. (1989). The voice of liberal learning(p. 16). Indianapolis: Liberty Fund.

Santayana . G. (1905/2005) The life of reason. https://www.gutenberg.org/files/15000/15000-h/15000-h.htm

Van der Veer, R., & Valsiner, J. (1991). Understanding Vygotsky: A quest for synthesis. Blackwell Publishing.
​
Vygotsky, L. S. (1986). Thought and language (rev. ed.). Cambridge. See also: https://www.marxists.org/archive/vygotsky/works/words/

I saw this picture, ‘Earthrise’, projected upon a screen being used to illustrate something in a conference talk.  The speaker said, perhaps as an aside, that of course we could not see this ourselves, you had to be a NASA astronaut or perhaps a multi-millionaire to see this for yourself. This set me thinking. Did the man who took this picture really see this himself? And is it really true that we have not seen this Earthrise for ourselves?
 
Wikipedia tells me that this picture, was taken by Bill Anders in 1968. But of course he took it with a camera through the windows of a spaceship. I mean that the picture was not just Bill’s picture but was the product of a collective effort. It is copyright to NASA not to Bill. Now we have robot craft taking pictures of the Earth from space, pictures of the surface of Mars and even moving pictures on the Internet of the state of the roads near you so that you can plan your journey without getting out of bed. Bill only saw the Earth from space with the aid of mediating technology. Mediating technology enables us all to see many things. We do not need to be physically present in order to really see the red rocks of Mars or the dust clouds of the centre of the galaxy or, indeed, the traffic on nearby roads.
 
When Neil Armstrong first walked on the moon I was 9 years old visiting relatives in Africa, camping with them and others in a large game reserve. There was a fire in the middle of the campsite. The moon was bright. The camp-site was fringed with trees and behind them a darkness from which came animal noises, mostly monkeys calling to each other. Around the fire I noticed a certain excitement and people pointing at the moon. An adult explained to me that men were walking on the moon. I was amazed. The people around the fire were of different genders and from different ethnic groups. None were American. Their excitement was not about an achievement by NASA or by the USA, but about something that, at that moment at least, everyone seemed to share. The feeling that we, the human race as a whole, had stepped outside of our home planet and looked back at ourselves. Whenever I see a picture of the Earth from space I get an echo of that feeling. The feeling that this is not just about an individual seeing something but it is more of a collective kind of seeing. Something that ‘we’ see, not just ‘I’ or ‘you’ or ‘him’ or ‘her’ but all of us.

In her claim that we could not see the Earth for ourselves unless we were an astronaut or very rich, the conference speaker was assuming a contrast between technology mediated vision – seeing a picture projected upon a screen - and natural vision – seeing with one’s own eyes. But when we look with our own eyes are we really individual?

Colour first appeared when we were in trees looking for fruit to eat. Being able to distinguish the fruit from the leaves and branches around it had an evolutionary advantage. The few mutant apes who could see in colour therefore had more babies that those who could only see black and white. Whenever I look at brightly coloured fruit in a tree I recall what I have learnt about the history of colour perception and I feel a part of something much bigger than myself. I realise that my vision is not just personal but collective, connecting me to a long line of ancestors all the way back to the original apes who, for the first time, climbing through the trees, were able to see fruit coloured red or orange or yellow, standing out from the leaves.

Learning to participate effectively in a dialogue is more than learning how to take turns, it is also learning how to see things from multiple points of view. To really listen to others implies learning what it means to be them. This kind of insight is necessary if you are to speak constructively in dialogues such that others respond to your voice, finding in it something that they can connect with and learn from because it feels to be already a part of them.
 
When we speak within a dialogue we have to use words already spoken and shaped by others, words with a history and meaning that we cannot control. Paradoxically, when we affirm our unique identity as a voice within a dialogue, when we say ‘I’, we are also affirming the dialogic space within which we speak and without which we would not be able to speak. We are affirming a shared history and culture.
​
In a dialogue identity as ‘I’ and identity as ‘we’ are intermingled. When I listen to you and respond out of that listening and you listen back then, even if there was no sense of ‘we’ there in the first place a sense of ‘we’ is brought into being.

[The Kingdom of God, 14th century, by Giusto de Menabuoi. in the Padua Baptistery]

Writing not as a Christian but as an educationalist, as someone interested in the wisdom that can be found in cultural traditions, I want to argue that Christmas points us to a kind of thinking that may well be relevant to the future of humanity as well as to its past and may even shed some light on the issue of who we are when we look at  Earthrise.

Christ is famous for claiming to be God, a claim that got him executed. But what does this mean?  ‘I am in the father and the father is in me’ (John 14:11) he reportedly said but there is still clearly some distinction to be made between him and God at times because he also said he did not teach on his own authority but on that of God (John 7:16) and he asked people not to call him good since there is only one who is good (Luke 18:19).  In a parable much quoted at Christmas he says:  ‘I was hungry and you gave me something to eat, I was thirsty and you gave me something to drink, I was a stranger and you invited me in, I needed clothes and you clothed me, I was sick and you looked after me, I was in prison and you came to visit me.’ (Matthew 25: 35-40).  He added that ‘whatever you did for one of the least of these brothers and sisters of mine, you did for me.’ So is Christ here claiming to be everyone? Not so much ‘I am in the Father and the Father is in me’ as ‘I am in everyone and everyone is in me’?
 
Yes I think that he is claiming that. And not only everyone but also everything. After all if the people did not sing out then the stones themselves would sing (Luke 19:40). For me this interpretation also comes out clearly when he says: “You have heard that it was said, ‘Love your neighbour and hate your enemy.’ But I tell you, love your enemies and pray for those who persecute you’ (Matthew 5:43-48).  It is our enemies that define the limits of ourselves. Our enemies are the people outside of the dialogue. Love is the experience of unity across an apparent gap of difference. Jesus’s call to love your enemies is therefore also a call to refuse to recognise any limits to the dialogic space and so any limits to the self.
 
Self can be limited by our socially conditioned imaginations to being all about my body or your body, my tribe or your tribe. These different ways in which we are taught to imagine the self have consequences. Jesus was offering us a different understanding of self identity, one which could, he claimed,  ‘set us free’. It is not so much a self-identity as a dying to the self in order to be re-born as everyone and everything. ("Truly, truly, I say to you, unless a grain of wheat falls into the earth and dies, it remains alone; but if it dies, it bears much fruit”). Maybe there are no separate selves at all and we are all, each one of us, just a temporary aspect of everything engaged in a dance of perspectives, ‘now inside’, ‘now outside’. This is perhaps to take the experience of a dialogic self, a self that identifies with the dialogue as much as with its own voice within the dialogue, and expand this experience to the whole of life. According to this view heaven is not elsewhere but here and now on earth if we allow ourselves to participate fully and freely in something bigger than our various bounded images of the self, for ‘the kingdom of God is among you’ (Luke 17:20-21).

​As individuals it is clear that we did not see the Earth rise over the moon just as we did not invent colour vision nor do we create the words we use and the festivals we celebrate. To participate in a culture, just as to participate in life, is already to be part of a thinking that is much bigger than us in all directions and has deeper roots than we can fathom. Too much of what passes for thinking these days is narrow-and technical. The kind of thinking that already assumes what is of most importance. As if we already know who we are and where we are going. Thinking about education and how we should teach our children requires bigger thinking, thinking that questions everything because everything is at stake. This is the kind of thinking that you might find yourself projected into if you listen responsively to the parables of Jesus. One key question that I think he was addressing some two thousand years ago is ‘who are ‘we’ really?'