Through the manipulation of open ended, concrete materials very young children learn about concepts (spatio-mathematical), which manifest the construction of primitive mathematical instruments: classifications, substitutions, symmetrical relations (correspondences), asymmetrical relations (seriation), the multiplication of relations, etc. These instruments are then used to express the acquired knowledge through the processes of making art: drawing, painting, sculpture and woodworking.
This work, which combined the concrete with the abstract, and the cognitive with the emotional, is used to communicate the child’s growing knowledge of the world he is ‘constructing’ out of experience. Furthermore this work embodied 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).
The mark of genius in the student is the ability to generalize the whole through simplification: then apply the symmetry — slides, reflections, rotations and/or inversions. May inter-disciplinary and intra-disciplinary cross-pollination continue
to enlighten our search for meaning and relevance in the arts and sciences.
–John A. Hiigli