How do we learn things?

By Lynnette Brock & John Siraj-Blatchford, SchemaPlay

This photo by Unknown Author is licensed under CCBY-NC

“One of the greatest mistakes of our day is to think of movement by itself as something apart from the higher functions… Mental development must be connected with movement and be dependent on it.  It is vital that educational theory and practice should be informed by this idea”.

Montessori, 1967: 141-142

Piaget (1969) saw it this way and, in more recent times, evidence from a broad range of cognitive science research has led many more to concur with Montessori.  Piaget argued that when we learn about something new, whether it is gaining an understanding of an object or phenomenon, natural or man-made, or even about how to solve a problem, we learn it not so much from what the object, phenomenon or what the solution looks like, from its figurative characteristics, but from how it behaves when we act upon it; from the affordances that it offers us.

Piaget explained this in his Mechanisms of Perception, “… cognitive structures, and structuring is brought about through an organisation of successive actions performed on objects” (Piaget, 1980: 23).

These successive actions that Piaget speaks of are now often referred to in early years’ literature, and are widely understood by pre-school practitioners as repeated schematic patterns of behaviour; they are actions that young children learn to accomplish and, because they have learnt them, they want to see how they fit or do not fit; how they can be applied or not applied in a variety of playful contexts and environments, and with different objects.  Children find these schemes a novelty and empowering.

Readers may be familiar with the work of Chris Athey (2007), where she defined the most common of these patterns of behaviours, witnessed whilst engaging in her Froebel Project.  Many of them are now familiar to early years’ practitioners across Europe as well as in New Zealand.  Operations such as ‘containing’, ‘enclosing’, ‘matching’, ‘ordering’, ‘positioning’, ‘transporting’ and ‘trajectory’ are often observed by early years’ practitioners and they provide a common language and taxonomy of the children’s activity in play.  They assist practitioners in appreciating what it is that the children are doing in their play in order that they may support and build upon it.

We have distinguished between figurative and operative (active) knowledge here but to appreciate how we learn through our actions upon the world, it is important at this point to consider the distinction Piaget made between two words – a ‘schema’ and a ‘scheme’:

“The terms ‘scheme’ and ‘schema’ correspond to quite distinct realities, the one operative (a scheme of action in the sense of an instrument of generalisation) and the other figurative” (Piaget, 1969, ix).

Observing children’s operational schemes is more valuable when we appreciate that they are a necessity to all learning: when a child first learns and is able to recall an object such as a bowl, this is not dependent upon their figurative recognition of what the object looked like, what Piaget termed a ‘schema’.  The learning originates, and is recalled, from their operational experience; what they found they could do with the bowl, from what Piaget termed the ‘scheme’.  In the case of the bowl, it becomes something understood as a ‘container’.  The implication is that every ‘golden nugget’ of knowledge must be understood as having two parts; one part figurative (the schema) and the other operative (the scheme).  In Siraj-Blatchford and Brock (2021) we elaborate upon this further and we note that neuroscientists have now confirmed this duality in their identification of ‘mirror neurons’, providing an even stronger empirical basis for what has become commonly known as ‘Embodied Cognition’ (Lakoff and Johnson, 1999).  As Montessori appreciated, “Mental development must be connected with movement and be dependent on it.”

Kramer’s (1975: 259) biography of Maria Montessori quotes the impression that Dr Montessori had of how children learn:

Children are “meeting new combinations of circumstances and overcoming them by means of aptitudes.”

This suggests that Montessori may have had some intuitive understanding that children apply their existing schemes to make sense of new schema contexts.  If you think about it, we do this every day when we come across something that we have never seen before.  To try and make sense of a picture or an object, such as the one below – we consider what its use might be (what the operational affordance would be).  Does it contain something, can it be used to transport something or to transfer something?

This photo by Unknown Author is licensed under CC

Another way to see how knowledge is dependent upon both ‘scheme’ and ‘schema’ is to consider how children learn about animals.  To support a child to distinguish between a cat and a dog we may make the noises that those animals make, re-enact their movements, or discuss what they eat.  It will be the operations or behaviours of the animals, such as their sounds (“miaow” or “whoof”), that helps them to distinguish between the two.

When we encourage a child to look at an object or a picture and we simply provide them with the name or the label, the child really does not understand what the object is.  As Hans Furth (1969: 11) puts it, when explaining the hindrance of rote learning, “A word is only as good as the knowing structure which uses it”.  The figurative verbalised or written name label, image and even the object itself is useless without providing a knowledge of what an object does or can be used for, or how it behaves.  Without the operational affordance we do not understand what it is and therefore the word will be meaningless.  This highlights the importance of naming the Montessori activities in operational terms when we first introduce them to children.

This distinction between a scheme and schema has not been appreciated in England.  Piaget himself was concerned about an unfortunate mistranslation of the two words from his native French into English (Furth, 1969).  Often in the UK, only one word, “schema”, is used in academic texts, and is applied interchangeably to refer to figurative and operative knowledge.  This is not helped by that the fact that these two words look and sound so similar, but it is important that we understand and appreciate that these two vital components are a necessary part of every ‘golden nugget’ of knowledge, if we are to provide an embodied education.  

“One of the greatest mistakes of our day is to think of movement by itself as something apart from the higher functions…”.

Montessori, 1967: 141

Montessori appeared to appreciate this; “Each impulse of the child is translated into action by means of the material” (Kramer, 1976: 259), meaning that the affordance has its origins in both the child’s body, and in the object they are interacting with.  She continues, “…and, working itself out in repeated exercises, trains aptitudes [i.e. the operational schemes], which will combine with aptitudes [more operational schemes that are used in combination] to form new activities later on, till finally we come to the highest and most complex human activities in literature, art, science, music, dance, drama.  It is all a web of phenomena” (Kramer, 1976:259) [our clarifications in brackets].

When an adult identifies the particular scheme that the child is applying (the affordance they have found) in a particular Montessori activity.  The operational scheme or schemes can be applied in a range of other meaningful contexts to support their learning.  The scheme or schemes can then be supported across the continuous provision and built upon (as they provide anchors for new learning), including in the outdoor environment, in the community and in support of sustainable citizenship, as well as in support of the complex operations: reading, writing, arithmetic, measuring that Montessori alludes to above.

Join us at the Connecting Montessori Europe webinar on Tuesday 11 May at 18.00 London time, 19.00 Amsterdam time, where we discuss emergence, and consider the scheme affordances of the Montessori materials in supporting children’s learning outdoors, in the forest, the beach, and in activities promoting the sustainable development goals. Register here.


Athey, C. (1990; 2007) Extending Thought in Young Children, London: Sage Publications

Furth, H. (1969) Piaget and Knowledge: Theoretical Foundation, USA: Prentice Hall

Kramer, R. (1976) Maria Montessori, United Kingdom: Biddles Ltd

Lakoff, G and Johnson, M (1999) Philosophy in the flesh: The embodied mind and its challenge to Western thought, New York: Basic Books

Montessori, M. (1967) The Absorbent Mind, (C.A. Claremont, Trans.) New York: Henry Holt

Piaget, J. (1969; 1980) The Mechanisms of Perception; translated [from the French] by G.N. Seagrim, London: Routledge & K. Paul

Radice, S. (2015) The New Children, Talks With Dr. Maria Montessori, England: FB&c Ltd

Siraj-Blatchford, J. and Brock, L. (2021)  SchemaPlay: An Embodied, Ecological and Child- Centred Approach to Early Childhood Education, UK:  SchemaPlay Publications

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