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The young child’s search for meaning through art is guided by intuition, through a basic awareness of space, at a level not yet formalized. The child who draws for the first time at an easel is performing a sensorimotor activity. This activity may be totally free, in the sense that he/she initiates a movement, which is observed as it develops. Or there may already be an image (in the mind), in which case the action is an internal imitation of previously known perceptions and/or previously performed actions. These actions are important in the mental construction of shapes, based on elementary topological relations: proximity, order and enclosure. They lead to and develop into operations that are at first concrete (five-seven years) and eventually abstract (ten-twelve years). To review the development of a concept of space begins with intuition, perception and sensorimotor activity, proceeds through the logic of concrete operations accompanied by the manipulation of objects and becomes complete through the logic of formal operation (twelve years).

Topological relations precede both projective relations (viewpoints) and Euclidean relations (measurement) with the latter two a manifestation of the first. The concrete operations of middle childhood are of a logico-mathematical nature and deal with similarities (classes and symmetrical relations) and differences (asymmetrical relations) or both (numbers). But long before children can perform simple operations (addition, subtraction, multiplication and division) with the aid of objects (concrete operations) or in their mind (formal operations) they must accumulate experience of a topological (sub-logical) nature through the manipulation of objects found in nature and in the early childhood curriculum at school (blocks, legos, cuisinaire rods, etc). The knowledge that they accumulate through these actions is expressed, developed and articulated through drawing and painting.

Through the manipulation of open ended, concrete materials very young children learn about concepts (spatio-mathematical) that manifest the construction of primitive mathematical instruments: classifications, substitutions, symmetrical relations (correspondences), asymmetrical relations (seriation), the multiplication of both elements and relations. These instruments are then used to express the acquired knowledge through the processes of making art: drawing, painting, sculpture and woodworking. This work, which combines the concrete with the abstract, and the cognitive with the emotional, is used to communicate the child’s growing knowledge of the world he/she is constructing out of the raw material of experience. It embodies a rudimentary form of the scientific method: the study and articulation of synergy, or the relationship of the parts to the whole.

A beginning understanding of the qualitative relations of topological space (proximity, separation, order and enclosure), and the expression of these understandings through drawing and painting, is essential to later mastery of the more difficult quantitative relations involved in projective space (viewpoints), affine relations (parallelism), and euclidean (three dimensional) space (measurement). Cognitive understanding develops when the child expresses and articulates his or her ideas through drawing and painting, through the development of the graphic image. The (spatio-mathematical) dialogue that accrues on the surface of the picture plane is responsible for the eventual attainment of the slanted line, found in the rhombus and used in the construction of numbers and letters.

All of these concepts and cognitive skills, learned through experience with concrete objects and articulated, rehearsed, and understood through the process of making art, form the foundation for the development of mathematics and science skills, and for writing. The exhibits in the physical gallery and at jardingalerie.org show the development of the child’s conception of space, of pre-mathematical structures, of writing and even in one case of story telling or text (Emma – 4.7 – Writing – E. T. Call Home).
 

 

 

 

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