January 20, 2021
In 1751 Diderot famously wrote in The Encyclopedias about a paradox that exists in the relationship between geometry, art, and mathematics. While we recognize that geometry is an important part of both math and the visual arts, we often think that it belongs principally in the domain of mathematics. Diderot believed, contrary to popular opinion, that geometry is dealt with in much more complex ways in the visual arts. While geometry done in mathematics is more sophisticated, it is cleaned up, simplified, and abstract. Diderot wrote, “It is clear that the elements of academic geometry (mathematics) constitute only the simplest and least complex elements of workshop (arts & crafts) geometry” (1751, Art, Vol. 1). In contrast to mathematics, the geometry done by the craftsperson or artist, requires extensive knowledge of a gamut of physical circumstances all at once or in combination ––elasticity, irregularities, temperature to name a few. The geometry done in the artist's studio is unpredictable, experiential, and experimental.
The idea that geometry belongs solely in the world of mathematics is still widely held today. My research works to circumvent the Diderot's paradox and establish a link between the visual art classroom and the math room through the shared computational language of shape and geometry.
My research looks at how children can learn advanced geometry in conjunction with learning to draw and design. Teaching children how to visually calculate what they see, that is, teaching children the skills inherent to drawing and sketching improves their ability to look closely and their ability to draw algorithmically more complex combinations of shapes and by extension, will enable them to communicate strong ideas and imaginations of beauty.
The ability to draw what we see is not a gift bestowed, but a nurtured relationship between our self and nature.
My doctoral research (2017-2020) was conducted within a fun, but rigorous drawing class. I had 85 participants in total over 5 research sites. My sites included one private school grade 3 classroom, one public school grade 3/4 split classroom, two home-schooled groups of multi-age children, and one after school art class in my studio. Much of the data analysis focused on children aged, 7 - 9 years of age who were either in grade 3 or grade 4 level of school.
I focused on this age range for two reasons:
1. Pragmatically, for statistical analysis this was the only grade level that had members in each of my sites.
2. In terms of cognition, there is something that happens in this age range where children stop drawing. It has been my experience that it is at this level of learning where I would hear children express that they either don't draw or can't draw.
I worked from the hypothesis that an observational drawing and design class focused on underlying shapes would do three things: 1) Help children draw and design better, 2) Improve children’s spatial reasoning and perceptual skills and, 3) Breathe new life into geometry for both visual art and mathematics education, bringing the two back together through their mutual love of calculating with shapes.
Students in my classes improved in standardized tests that measured visual motor integration and spatial manipulation tasks, such as the Beery VMI. Qualitatively, this research demonstrated that their drawings improved dramatically when they were taught how to use an approach based on shapes, where they created and followed algebras to manipulate shapes to match what their vision. Children were able to render what they saw with nuance and sophistication. Their ability to manipulate, interpret, and see in multiple perspectives calls into question notions of stage development theories that place cognitive limitations on children’s vision based on age alone.