Let us start with a little experiment:

1. Draw form 1 enlarged and complete it freehand so that it becomes symmetrical. Can you observe what enables you to do this?

2. Draw form 2 enlarged (in the indicated position) and draw in the axes of the symmetry. How do you manage to do it? 

Studies have shown that when primary school children are asked to draw axes of symmetry in a given figure, most of them turn the page so that the axes of symmetry fall in the (outer) symmetry plane of their own body or at least of their own head. The perception of symmetry is fundamentally related to our own body position, which is essentially perceived by the sense of balance and controlled by the muscles. Very briefly, we can say: the (vertical) straight line drawn in Waldorf schools on the first day of school objectively confronts the child with their own actively generated uprightness. Expressions such as being straight with someone, having an upright character and similar indicate that the experience of uprightness has many more references to soul experience than a mere physical meaning. In comparing forms 3 and 4, anyone who does not block themselves can explore these relationships.

How do we grasp forms?

The most frequent but naïve answer will be: I can see them. Obviously this can only be half the truth because if the perception of forms – like the perception of colour – were necessarily connected to the sense of sight, blind people should not be able to perceive shapes. As we know, this is not the case. So what is going on?

To answer this question, it is helpful to distinguish between sensory organ and sensory function. The eyeball with the associated muscles, the corresponding nerves and blood vessels is a sensory organ that is a carrier of very different sensory functions: it is sensitive to heat, sensitive to touch, perceives colour and, last but not least, is a motor organ whose movements are controlled and steered by the kinaesthetic sense. Through the motor activity of parallax, it grasps the third dimension as if with gripper arms.

How, then, does a blind person grasp a form? In principle, it is no different from a sighted person: they run their hands over the shape, thus grasping the form through their own movement.¹ Sighted people do not need to probe with their hands. They move along the differences in colour and brightness of an object and its surroundings with their gaze, guided by purposeful attention (intentionality) to a perceptual area, and perceive the form through this movement process.

In doing so, we can become aware of a fundamental difference between perception of a colour and the grasping of a form: the colourfulness of our surroundings is more or less given to us. To grasp a form, we have to become active ourselves. To exaggerate, we can say: form is not there for us if we do not create it through our own activity.

Free form drawing or graphics software?

Many programmes are of course available today with which a wide variety of shapes can be created, coloured, changed and reassembled in a short time. Once I have drawn a shape on the computer, it is easy to mirror, rotate or edit it in some other way. A few clicks are all it takes, but the amount of personal activity is significantly reduced.

The best way to gain experience of this is to do it yourself: draw some of the forms 5 to 8 on a sheet of A4 paper as carefully as possible and mirror them on the dotted vertical axis without any other aids and observe yourself doing it.

Done with a class 2 or 3, various difficulties can become apparent – in addition to wonderful results. For the teacher who is interested and trained in special education, it is precisely these difficulties that indicate where help is needed. It is not primarily a matter of achieving better results in a short time by using some kind of aid but of recognising the causes of these difficulties. Form drawing itself can be effectively used therapeutically.

Educational note

Each of our physical or mental activities has effects in two directions: a product – also in the form of a service or the mental solution to a problem – can be delivered to the outside world through them. Its value will essentially mean something to the recipient. Equally, however, every activity has an effect on the person who has carried it out, be it that they strengthen or weaken their physical constitution, be it that they acquire new mental abilities.

General education schools will always have to pay attention to what repercussions a physical or mental activity has on the development of the overall constitution in the broadest sense of the child. The younger the child, the more the focus is on such constitutional development. The “products” produced by pupils (essays, text translations, solutions to tasks in mathematics, knitting in handwork work, etc.) usually have no or very little social significance. The focus is rightly on skill development. Whereas in a company it is usually a matter of satisfying customer wishes in a qualitatively acceptable, quick and inexpensive way, school has to develop the basic skills of young people which are the basis of all other activities.

Of interest in this context is a recently published longitudinal study from May 2021 whose findings can be summarises as: “Early motor difficulties in preschool children had significant effects on their academic achievement and psychosocial maladaptation up until the sixth grade. Gross motor difficulties in preschool were associated with the later peer problems and worsened emotional symptoms.”²

Form drawing is certainly not a panacea for all observable developmental disorders, but in an increasingly sedentary society it prevents undesirable developments that can lead to serious disadvantages in later life. From a constitutional point of view, drawing forms intensively trains gross and fine motor skills, eye-hand coordination, strengthens the connection between the sense of balance and the kinaesthetic sense and has a wealth of developments derived from it. For example, the drawing of braided ribbon patterns, which is often undertaken in class 4, can be seen as a first step towards the development of active inner spatial perception (spatial intelligence³) through the requirement to see the two-dimensional drawing in three dimensions through inner activity. This is not about copying a picture but about active thinking or imagining in the third dimension and representing this in two dimensions (form 9). It is of course easy to admit that not every drawn shape has the same effect in the present sense. Pressing down keys is also a motor activity. However, if we compare it, for example, with the drawing of the forms reproduced here, its lack of movement is immediately apparent.⁴

Form drawing as artistic training

If we portray the importance of form drawing only as training gross and fine motor skills and a few other abilities, we are left with the bitter taste of a medicine with numerous side effects. Being able to grasp, describe, compare, remember and draw forms disregards the educationally always necessary emotional involvement. Consider the devotion and joy with which pupils colour in successful sketches. If a sense of beauty for the language of forms lives in the teacher, a whole class can welcome a successful new form with great warmth. If, step-by-step, it is given structure, walked, drawn large in the air and finally put on paper, first delicately and then more and more vigorously, a joyful creativity sweeps through the whole classroom. The intellectual pallor of abstract teaching theories collapses before it like a flash in the pan. (See form 10: Braided ribbon pattern as a sketch for a piece of jewellery).

We may ask whether, in an emotionally colder and colder world, the development of feelings and a sense of beauty should still be meaningfully cultivated. In any event, from an economic point of view, the ability to create shapes in an appealing way is not meaningless. As everyone knows, the design of a product plays an important role in the purchase decision (form 11 + 12).

Design for industrial products today is of course done with computer assistance and implemented in manufacturing, but creativity is related to skills that need to be gained in early stages of development and in the context of social learning. The epidemic deskilling effect of unproductive pseudo skills was described decades ago.⁵ It is not computer programmes that create innovation, but people who can use the modern tools creatively! Education is more than being able to solve tasks set by learning programmes taking account of the given possibilities.⁶

About the author: Dr Ernst Schuberth, studied mathematics and physics, was a class and upper school teacher at the Munich Rudolf Steiner School. Appointments at the Westfalen-Lippe College of Education and Bielefeld University. In 1978 founded the Freie Hochschule Mannheim. Worldwide teaching activity and numerous publications on mathematics teaching. www.ernstschuberth.de

1. A blind pupil, whom I had to prepare for the university entrance exams from class 11 onwards, had a fellow pupil draw all the figures on her hand. She grasped the figures by attentively following the touch impressions in her imagination. We do this in the same way when a shape is drawn on our back. We are dealing with an internalised activity of the kinaesthetic sense. Detached from all external impressions, we carry out such internalised sensory activities, for example, when dealing with geometrical shapes in the tableau of ideas. Such internalisation is the second step towards actual geometrisation, in which judgements (theorems, propositions) are made about the relationship between geometrical figures.

2. “Fine and gross motor skills predict later psychosocial maladaptation and academic achievement”. In: https://pubmed.ncbi.nlm.nih.gov/33558106/

3. https://www.thoughtco.com/spatial-intelligence-profile-8096

4. For people familiar with the geometry of free curves, the singularities that occur (spike point, beak point, inflection point, etc.) are characteristic of different curve forms. Interestingly, these are the places where pupils can often advance in motor skills. See: Ernst Schuberth, Das Formenzeichnen als tätige Geometrie in den Klassen 1 bis 4, Stuttgart 32021

5. For example in Walter Volpert: Zauberlehrlinge. Die gefährliche Liebe zum Computer, Weinheim 1985

6. See also the noteworthy references in: Thomas Sattelberger und Sven Gábor Jánszky, 30 September 2021, https://www.capital.de/karriere/fuer-eine-kulturrevolution-der-bildung