Learning and meaning development in six-year-old children using the example of bridge building
By Hannelore Schwedes | University of Bremen
The starting point for this contribution are video recordings of various children who solve the problem of building a bridge over a river (a blue strip of paper) with cuboid wooden building blocks (approx. 5 x 10 x 2 cm) so that various animals, including an elephant, can later cross the bridge. So the bridge has to carry the weight of an elephant.
The video recordings show different solutions for this task and different experienced bridge builders. The central learning experience is the discovery of the principle of the counterweight in order to store cantilevered components stably.
Three processes of problem solving are to be described and the children’s actions, learning and development of meaning are to be discussed. The three short sequences of a task solution were selected, on the one hand, to discuss different dimensions and differentiations of the determination of learning and the concept of meaning, on the other hand, the formation of a new concept, the development of the idea of the counterweight, can be observed in one example and discussed in the context of a more general hypothesis relating to learning through the use of body analogies.
Three boys (Peter, Kurt and Armin) build a bridge according to a different (raw) design, and they also show different technical skills and experiences in dealing with the building blocks. One boy learns the intended principle of the counterweight, the second mastered the most diverse possibilities of creating balance and thus also the principle of the counterweight, the third pupil remains despite multiple failures of his construction with his initial picture of the bridge arch, but does not find the principle of the counterweight, which would exist in the mutual support of the two partial arches – but also still the adhesion (friction) of the individual building blocks to each other would have to include.
Peter’s building an arch bridge. He lays the building blocks lengthwise parallel to the river and lays them stone on stone, each following one always shifted a little more towards the middle. He builds symmetrically, from both sides of the bank, so that the two sloping towers meet in the middle. Although his sloping sides of the bridge collapse several times, he does not change his construction, e.g. by placing the building blocks perpendicular to the edge of the bank; then he could be successful with his construction, but the bridge would then be (at least) narrower. But Peter seems to have an unbreakable confidence that his construction has to work, the success for him seems to be above all a question of the careful layering of the stones on top of each other – similar to the house of cards, which also collapses if the cards are placed on top of each other clumsily: The task is finally simplified by the teacher by reducing the width of the river, so that Peter finally arrives at a successful conclusion to his plan. It is astonishing to observe the high concentration with which Peter layers the blocks on top of each other and the support that Peter gives his building with his hand. He nestles his hand to the planned curvature, not supporting the uppermost stones that were last placed, but intuitively correct, the stones from the middle to the lower third of the arch of the bridge, for somewhere there is also the place from where the sloping tower tears off and falls over. All in all, however, the impression remains that Peter sees the successful design in the fact that each side must keep its own balance, as with the task of building the tallest possible tower.
Armin is a very agile farmer. Its construction of the bridge is more like a gate or archway (see Fig. 2). This is further emphasized by the block which he places vertically in the middle of the bridge or gate at the top. Only when he is reminded that the animals should cross the bridge does he remove this block again. Armin also builds his bridge symmetrically, from both sides of the river bank. To cross the river, the stones are arranged perpendicular to the flow direction.
The principles of balance, equilibrium and counterweight are familiar to him. A building block is pushed forward only a short distance above the supporting point so that the weight of the block on the other side is still large enough to carry the next vertically mounted block. A tilting of the building block at the next step, just perceived with the eyes, is immediately answered by placing a building block as a counterweight.
Even when placing the top row of blocks, the bricks are first placed in the middle, and then later, when two more blocks are at hand for the counterweight function, they are moved forwards towards the middle of the river.
The most interesting is Kurt’s construction process, because he is able to follow how he invents the idea of the counterweight. Kurt first builds a massive bridge bearing, then lays the bricks for bridging across the river, has laid another brick behind the bridging blocks (quasi as an abutment) and hopes to give his bridge sufficient stability by compressing the two bridging blocks with the help of the entire bridge bearing. However, its construction does not hold, the bridging blocks tilt downwards towards the middle of the river.
Three children, three task solutions – but also three learning processes?
Kurt begins anew, now supports the bridging blocks with his hand from the middle of the river, deliberately, senses, and completes his bridge construction on a trial basis and, weighing a block he is holding in his hand, places it on one bridging block as a counterweight and then immediately lays a second brick on the opposite bridging block as a counterweight. Now two more blocks are inserted parallel to the first to widen the bridge and finally more blocks are placed as a counterweight to increase the stability of the bridge.
For the time being, let us use the definition of learning common in educational science as experiential behavioral change!
In the first attempt we will probably only say with Kurt that he has learned something, because as pedagogues we usually pursue (more or less) concrete teaching goals by setting a task, here the development of the concept of counterweight.
In this context Armin – although he mastered the task excellently – did not learn anything, nothing new, he already knew everything, he was too „smart“. Peter didn’t learn anything either, he didn’t master the task, he didn’t develop the idea of the counterweight, he remained „stupid“. Only due to a „teacher“ invention, which created simplified initial conditions, was he able to complete the task satisfactorily for himself. This definition of learning as an intended change in behaviour is problematic insofar as it relates primarily to teaching objectives (of the teacher), not to the learner’s objectives (or only insofar as the learner has succeeded in making externally set objectives his own). Teaching objectives easily obscure the observer’s view of the perception of behavioural changes that were not intended, but nevertheless took place and provide important keys for understanding learning processes.
If the students were asked if they had learned anything, they would probably answer the question yes, we have learned to build a bridge, and rather do a classification in the direction much – little learned according to their assessment of the difficulty of the task. Their (subjective) idea of learning could be formulated as follows: „If I have learned something, I can/know something that I could not do/know before“.
However, the observation is learnt – not always learned with a view to proving a concrete goal of action achieved or to be achieved.
This determination of learning by learners, which is primarily oriented towards the achievement of action goals, is consistent with the description of learning as experiential behaviour change in that it also refers to two points in time (before – after), namely a situation in which a certain ability was not (yet) available, a (expected) successful behaviour was not (yet) shown and a second situation in which a new behaviour is used, which then usually leads to coping with the situation. In the meantime, experiences were made (observations, exercises, trial treatments, experiments, thinking) that stimulated the new behaviour.
The educational definition of learning as a change of behaviour reflects the situation that learning cannot be observed directly, either by the learner himself or by an outsider. Learning can only be accessed indirectly. We observe certain changes in behaviour under certain conditions (exercises, tasks, etc.) and conclude that learning has taken place as a result of external influences and the learner’s reactions to them, i.e. interactions with the environment.
When pupils say that they have learned to build a bridge, this can of course mean very different things in detail, e.g.: to design a plan for a bridge, to implement a plan, to realise a plan with given materials, to know the properties of the blocks (weight, friction, adhesion, centre of gravity), to be able to use blocks in different functions as a foundation, as a support, as a connection, as a counterweight), to have experience with gravity and equilibrium, to be able to assess the load-bearing capacity of a structure, or simply to say that I have successfully mastered difficulties or problems in the task of building a bridge. I hadn’t built a bridge (or any such bridge) before, I didn’t know if it would succeed, now the bridge is there.
If we as observers once again follow the development process of the bridges, we will consider such learning outcomes to be plausible, but they cannot be observed directly because of the available excerpts. Let’s spend another moment with Peter. Untiringly he layers the building blocks carefully again and again, shifted diagonally on top of each other. He takes great care, aligns the stones several times parallel to each other again when they have slipped somewhat – trying not to bring down the whole work by manual clumsiness, as in the construction of a house of cards. Peter’s tolerance for frustration seems enormous, showing neither anger nor impatience when his construction collapses again and again. What did he learn? Did he improve his skill in piling up building blocks, did he learn that one must not build bridge arches too wide so that it is possible? Has he discovered limits for diagonal layering of the stones, does he know where the slope can be supported most effectively, or has his self-image – I am (k)a (particularly) successful bridge builder – changed? With the exception of the increase of the skill in building, we can assume all this, but not say with certainty, because we lack the observation situation with the proving for the new learned behaviors.
When we talk about learning, we also associate it with a permanent change in the brain, which leads to the expression of the new behavior due to the behavioral control by the brain. Varela describes learning as such a modification of the brain structure which, due to the interaction of the organism with its environment, leads to a change in the way in which the organism is coupled to its environment. (The bridge arch will be narrower next time.)
Learning serves to expand the behavioural repertoire for viable adaptation to the environment so that the human being (organism) can respond adequately (in terms of well-being/preservation) to environmental events (the need to build a bridge to satisfy the teacher or actually cross a river). Interaction with the environment is always accompanied by brain activity, i.e. electrical activity of nerve cells. If one follows Hebb’s hypothesis that the firing of neurons and the transmission of impulses is linked to a change in the coupling between the neurons involved, every interaction with the environment leads to a change in the brain structure and a change in the brain structure leads to a change in behaviour.
Here the question arises whether every brain activity is actually linked to a change in the linkages between the neurons, i.e. learning always takes place in principle and we can only as observers not perceive the resulting behavioural changes because they are too subtle or whether brain processes can be divided into classes in which everything remains as it is and those with linkages. A third alternative would be conceivable, namely to make a subdivision according to processes with strong or rather small modifications. The change of the coupling between neurons then deepens according to a kind of saturation model, so that only small to smallest changes of the coupling strength occur with multiple recurring orbits between the same neurons.
In „practice“ we know this phenomenon, after multiple repetitions the ability or perfection only increases very slowly, but also for the status change of our knowledge, as Schütz-Luckmann describes it, such saturation curves could play a role. Learning is subject to a status shift. All knowledge elements have only temporary validity, they can be problematized. The more they have proven themselves, the less they are called into question. Criteria of a high / low status are familiarity, determination (authority), clarity, credibility of a knowledge element. They are generally no longer changed, they often remain the same for a lifetime, they form the „sedimented store of knowledge“.
With the question of the emergence of meaning we more or less automatically encounter the analysis of learning processes; but are learning and meaning development really identical? Is every learning really linked to the construction of new meaning?
Varela distinguishes between learning and the emergence of meaning. While learning involves a change in neuronal connections in the brain, meaning is an emergent phenomenon of brain activity that occurs as a sign of reaching an attractor state in the course of self-organizing neuronal activity. Meaning can only be created and assigned context-dependently. It arises from the interaction of perception and action in concrete life situations. Action and perception influence each other in the circular processes of expectation, perception and action controlled by expectation.
According to Piaget, the training of sensorimotor skills is the basis for all higher forms of learning. He has provided detailed descriptions of the childhood development of sensorimotor activity and proposed circular processes as organizational units for the assimilation of experience. He has thus had a lasting influence on our idea of the development of intelligence. The basis of all later cognitive development is the expansion and differentiation of our sensory-motor abilities. Our (early) body experience is used in the course of the subsequent cognitive development as an analogy for the opening up of further areas of experience. This thesis is explained, among others, by Mark Johnson in his book „The Body in the Mind“ for the area of language development.
If one imagines that, when using a body analogy, the neuronal trace of perception and movement of the corresponding sensumotoric unit or of the associated sensorimotor schema is activated in the brain without actually executing the (controlled) movement, one can think of the experience opening effect of the analogy formation in such a way that in the course of a mental understanding process new neuronal patterns (follow) are coordinated with the activity patterns called by the body experience and in this way new meaning arises (usually very effectively) so that the now interacting neuron groups cause the emergence of a new global state on the basis of the initial sequences (Varela).
In my opinion, the learning processes of children building bridges shown in the video now provide extremely interesting material for studying cognitive processes; they could contribute to examining our theoretical ideas about learning and meaning formation, to differentiating more precisely between learning and meaning development, and to discovering learning rules and mechanisms of meaning construction. The observation of the manual activity of children seems particularly fruitful to me, because here the transition from cognition in the sensumotor area to predominantly mental activity, to pure mental actions, can be captured and thus also examined.
In particular, the process of Kurt’s task solution seems to me to be productive for our purposes. In this example we can follow the birth of the idea of the counterweight in quite detail, the construction of a mental concept, the emergence of meaning. We are referred to the study of the use of body analogies as perhaps a very effective tool for learning and developing meaning.
Let’s recapitulate Kurt’s trial once more.
After the failure of the first construction design, Kurt prevents the bridge from collapsing again by hand support. He keeps the planned arrangement of the blocks, the optical idea of the bridge and searches for a new construction idea, after he had to discard the old construction, to achieve the necessary stability by compressing the blocks, because of unsuitability. Kurt completes his bridge construction plan on a trial basis, while continuing to hand replace the bridge’s missing support. He feels the weight of the protruding blocks, their tipping inwards and sees their slight lifting on the bridge bearing. For a long time Kurt stays like this, slightly moving his supporting hand up and down – as if thinking and thinking. The initiation of the idea of counterweight could arise precisely in the previously described coordination of mental activity with the activated neuronal trace of the body experience of counter-pressing, for the purpose of balance, of (counter-)holding.
A result from Dieter Schmidt’s study on the concept change could point in a similar direction, in which the breakthrough to adopting the intended concept by activating the bodily experience of „pressing with constant force“ succeeded. (The constant force did not lead to constant, but to increasing speed of the moving liquid).
U. Maichle has also pointed out the concept-forming power of body analogies in her investigations of student ideas in the theory of electricity. Giving, taking and distributing schemes structure the students‘ experiences with electrical circuits, not the functional connections of Ohm’s law.
The thesis that body experiences organize mental processes is supported by diverse observations and experiences from other areas. Aebli describes thinking as the ordering of doing, Vygotski describes the transition from outer to inner speech as an important part of learning processes. Gestalt therapy activates past (emotional) events by adopting certain postures and tensions, by strengthening certain gestures and movements. Wilhelm Reich came up with the idea of body or muscle armour, which could be softened or dissolved to bring frozen psychic, inhibitory constellations into flow and thus change them. Varela uses the term „embodiment of mental events“ based on research by Mark Johnson, who finally shows how our language is permeated by images and metaphors based on bodily experiences and how our description of reality is shaped by the perception of our body, i.e. our bodily experience.
At the latest at birth, the human organism learns to distinguish between itself and something other than itself, its environment. The images and schemata created on the basis of body perception can now be used to structure and understand the environment.
Excursus: „The body in the mind“
Johnson uses the schema term used by Ulrich Neißer, which in turn developed it further from Piaget’s circular reactions.
A scheme is bound to perception and motor programs. It is the part of a whole hearing circle that is internally in the perceiver. It is modifiable through experience and in a „certain“ way specific to what is perceived. The scheme takes up „information“ as it becomes available on the sensory surface, and it is itself changed by the „information“. It directs movements and exploration activities (such as the Piaget Greif scheme) to make more „information“ available, which in turn further modifies the scheme. From a biological point of view, a scheme is part of the nervous system. It is a kind of active arrangement of physiological structures and processes. It is not a center in the brain, but a whole system that includes receptors and affectors as well as feedback units and affectors. The emergent property resulting from the activity of the related components, namely the meaning, also constitutes the schema in differentiation from possible other schemata and activity circles in the brain. A scheme is not only a plan, but also the executor of the plan, it is a pattern of action as well as a pattern for action.
To the central position of importance of the constitution of schemata fit studies that Anderson reports to prove the superiority of our memory for meanings. People usually grasp the meaning of a message, which they retain, but they do not remember or only poorly remember its literal formulation (the literal formulation is reconstructed from the meaning and possibly deviating from the original sentence). In terms of visual perception, the task of tracing Drudel also revealed that it was primarily the meaning of an image that was captured, while details of the representation were not registered separately in the first place, or at least not remembered. Also the tracing of the Drudel had the character of a reconstruction process starting from its meaning.
As one of several examples of the effectiveness of body schemata in our thinking, Johnson presents the in-out scheme. The in-out scheme is based on our encounter with containers and boundaries. It represents a class of basic body experiences and structures our thinking in wide areas. We experience our body as a (three-dimensional) container into which we can put certain things like food, water, air and from which certain things like sweat, air, blood, excrement, urine come out. In the same way, from the very beginning we experience our body to be inside and outside containers, as in the uterus, from which we are pressed at birth, or when we enter and leave rooms, vehicles, vehicles.
The in-out scheme, like other schemes, is not propositional. It is simple, but has enough internal structure to generate conclusions and prevent others, it supports our experiential ordering activities by making the distinctions typical of the scheme. The in-out scheme can best be illustrated by the following picture.
It contains the cross and thus the position within and the triangle and thus the orientation outside the circle, which stands for container and boundary. The in-out scheme structures the space into interior and exterior areas and allows for changing viewpoints, looking from the inside to the outside or from the outside to the inside.
Five important structural features characterize the in-out scheme:
- The experience of abstinence
It also includes protection against or resistance to external forces. If a pair of glasses is in a case, it is protected against external forces.
- The Experience of Containment
At the same time it contains the limitation of the forces in the container. When I am in a room or in a straitjacket, I am hindered and limited in my powerful movements.
- Due to the limitation of forces by the container, a contained object has a relatively fixed local position. A fish is in the aquarium, the cup is held in the hand.
- The relative local fixation in the container also means that the contained object is either accessible or hidden to the observer’s gaze, depending on the observer’s point of view or the nature of the boundary.
- It implies the transitivity of the containment relation. If B is in A, then everything that is in B is also in A.
Our actions in daily life are full of in-out orientations, as we can easily verify at the linguistic descriptions. In the morning we wake up from a deep sleep, jump from our feathers into the room, jump into our clothes, stretch out our limbs and go out of the bedroom into the bathroom in dizziness. We look into the mirror and see ourselves staring out of it. We reach into the toilet cupboard, take out the toothpaste, push the toothpaste out of the tube, put the toothbrush into the mouth, brush the teeth in a hurry and flush out the mouth.
Similar orientations and structures of our experience can be found in the diagrams of up-(warts)-down(warts), near-far, left-right, front-back, (out-)to-way.
The spatial in-out orientation gained from the body experience can now be metaphorically extended to other areas of our thinking and acting. For example, a story, a race, or a state can be perceived as a container, as can be seen from the following formulations. Tell me your story again, but leave out the smaller details / I get out of the race / Whenever I’m in trouble, it helps me out. Or the verbs can omit, (her)reach out, (her)exclude physical actions as well as metaphorically refer to mental actions. What is physically picked out are spatially extended objects, what is metaphorically picked out are abstract, mental units.
The far-reaching function of body schemata for the structuring of our experience and (thus) for the construction of meaning shown by Mark Johnson seems to indicate that we are dealing here with a basic mechanism of learning. It remains to be investigated on the one hand how body schemata are developed exactly, on the other hand whether other analogies can be traced back to mechanisms in the use of body schemata as a means of understanding complex facts.
John R. Anderson.
Spectrum, Heidelberg 1988
The Body in the Mind
University of Chicago Press, Chicago/London 1987
Jean Piaget, Bärbel Inhelder
The psychology of the child
Walter Ölten, 3rd edition 1976
Francisco J. Varela
Cognitive Science/Cognitive Engineering
Suhrkamp Frankfurt 1990
Francisco J. Varela
General principles of learning within the framework of the theory of biological networks
in: Siegfried J. Schmidt: Memory
Suhrkamp Frankfurt 1991 p. 107
Bedeutungsentwicklung und Lernen, Band II, Seite 93 – 107, Herausgeber:
Forschergruppe „Interdisziplinäre Kognitionsforschung“ der Universitäten Bremen und Oldenburg,
Zusammenfassung des Seminars in Wremen vom 11./12. Dezember 1992