Written by Rebecca Mitchell and Andrea Kantrowitz
Focus for a moment on an object in front of you. How do you understand its shape? How would you represent it by drawing it? Imagine turning or rotating it. What would it look like then? How could you create something with the same shape?
You’ve just utilized spatial intelligence, your capacity to analyze and transform visual and mental imagery in two and three dimensions. This capacity is fundamental to both math and art, and a has been found to be a key indicator in students’ long-term academic and professional success. A growing body of research in educational psychology and cognitive science is looking at ways to enhance spatial intelligence, such as a recent study which showed that spatial training improves 6-7 year old children’s math calculation.
When we look at and create art, we are exercising spatial intelligence to analyze and construct objects and images. Rich experiences with works of art have been shown to significantly enhance student math achievement, as documented by the Framing Student Success program that studied the effects of standards-based instruction that integrated high-quality visual arts, math, and literacy content in three high-poverty New York City Public Schools. These findings support a growing trend in K-12 programs across the country to merge arts instruction with science, technology, engineering and math (STEM) education, pioneered by Rhode Island School of Design’s STEM to STEAM initiative.
How can the excitement around the potential of the arts to contribute to STEM education, along with current research on spatial ability be shared in an art museum setting, so that PreK-12 teachers can bring the ideas into their classrooms? Here we’ll share the activities and discussions that we designed with this aim. The two-hour gallery session was a part of a week-long teacher institute, VAST (Visual Arts and Sources for Teaching) held at the Philadelphia Museum of Art this past July. The overall theme for VAST was integrating art across the curriculum. Our session was led by Andrea Kantrowitz, Assistant Professor at Tyler School of Art, Temple University, who co-wrote and implemented the Framing Student Success curriculum; Rebecca Mitchell, former Manager of Teacher Services at the Philadelphia Museum of Art; and Lynda O’Leary, Distance Learning Coordinator at PMA.
Through a series of structured activities (individual, small group, and large group) – looking at art, drawing, creating sculptures, discussing, and choreographing a short dance on a work of art (yes, you read that right!), the teachers engaged their spatial thinking skills to think and create in two- and three- and even four- dimensions.
The setting: Temporary exhibition, Minimalism in Motion at the Philadelphia Museum of Art and permanent collection galleries
Audience: 80 PreK-12 teachers (in groups of 20 at a time)
Format: 2 hours
Materials: stools, sketchbooks, pencils, grid paper, scissors, circular stickers (we used mailing stickers)
Translating 3-d into 2-d:
After a short introduction to the Framing Student Success study and some research findings about spatial thinking, the teachers began their first activity. With pencils and sketchbooks in hand, the group spent 10-15 minutes drawing Robert Morris’s Untitled (Battered Cubes) from 1970, a piece made up of four large cube-like objects. Andrea explained that there was no “wrong” way to draw the sculptures, and that a variety of approaches would be beneficial to our discussion later. Since there were art teachers and classroom teachers in each group, we didn’t want anyone to feel self-conscious about their drawing ability. Andrea emphasized that it was the thinking and problem solving that was most important, not how “accurate” the drawing looked. The teachers sat wherever they felt comfortable, and drew the sculpture from whatever angle they preferred.
The teachers then watched a minimalist dance performance, choreographed by Lucinda Childs and filmed by Babette Mangolte in 1973, Calico Mingling (available here: http://ubuweb.com/film/mangolte_calico.html) and notated it however they wanted to – through sketches, notes, or some combination of the two. Again, the goal was to observe closely and record these observations with pencil and paper. In the Childs piece, the dancers move around and through a grid pattern on the ground, located at Robert Moses Plaza at Fordham University.
Many ways to solve a problem:
We gathered the teachers back together and placed the drawings of the sculpture on the floor. After a walk around the circle to look at all of them, we discussed the variety of approaches – while some people showed multiple viewpoints in one drawing, others focused on what they could see from their vantage point. Next we looked at everyone’s notes/sketches of the dance, which revealed even more variety. Some people focused on one dancer’s movements, while others watched for overall patterns among all of the dancers. Still others counted steps, traced arcs of the movements, or looked for relationships between the dances and the grid below their feet. All of these approaches yielded successful results, and the variety of solutions enriched the group’s understanding of both the sculpture and dance. We discussed the challenges and strategies to translate three-dimensional objects onto a two-dimensional surface, and the added complexity of movement and time.
Building it out again: three dimensions
Now it was time to experiment with creating something three-dimensional from a two-dimensional material: paper. Working with a 1 1/2 inch dot grid on an 8 1/2 x 11 sheet of paper, a pair of scissors, and small circular stickers, teachers created sculptures. No specific instructions were given except to create something three-dimensional based on the grid. The teachers cut, folded, and taped. Discoveries were made, and sculptures were adjusted. They learned what worked and responded to their new knowledge as they continued to build. As expected, this exercise resulted in a wide range of sculptures – size, shape, and orientation. We displayed the sculptures in the center of the room and discussed the process and results.
Introducing time: the fourth dimension
Happily, there was a Carl Andre sculpture installed in the exhibition, which consisted of 17 copper squares, arranged in a line on the floor. Another grid! This gave us, the facilitators, the idea to culminate this part of the session with physical activity, something we thought would also benefit students when these ideas were translated into a classroom. Andre’s sculptures are meant to be experienced by walking over, around, and on them. Taking inspiration from Childs’s dance, we split the larger group into groups of 4-5 teachers and gave them 10 minutes to create a dance on and around the sculpture. Although coming up with choreography was a new experience to many of the teachers, they embraced the challenge and had fun working together. Again, the final pieces showed great variety:
Some moved in grid-like movements: forward, backward, side-to-side, while others incorporated more organic movements. Some were in unison, others had each dancer moving in a unique way. All utilized the length of the sculpture and responded to its structure.
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On a concluding walk through the galleries, we took note of how artists throughout time and place use the grid to organize space. For example, the use of one-point perspective in a Canaletto painting or the incorporation of multiple perspectives in an 18th century Japanese screen. From grids on floors, to decorations on the ceilings, to paintings, drawings, decorative arts, and sculptures on view, it became clear that grids abound in art and architecture. We began to consider the world around us in new ways and recognize underlying structures that order our built environment.
These exercises drew the teachers out of their comfort zones and encouraged them to engage in creative play – looking, drawing, creating, dancing, and discussing. They considered spatial relationships from several perspectives and through different means. It is our hope that the teachers left the session with practical ideas for the classroom, an enriched understanding of spatial intelligence, and a new appreciation the interconnectedness of art across the disciplines.
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About the Authors
REBECCA MITCHELL is the former Manager of Teacher Services at the Philadelphia Museum of Art, where she taught students in the galleries, organized teacher programs, and wrote teacher resources (to view the PMA’s teacher resources, please visit www.philamuseum.org/teacherresources). She has a B.A. in art history from Smith College and an M.A. in art history from the University of Delaware. She currently resides outside of New Haven, CT, where she is spending time with her two young children, but remains active in the art museum education community.
ANDREA KANTROWITZ, EdD, is an artist and researcher, who has lectured and given workshops internationally on art and cognition. As the director of the Thinking through Drawing Project at Teachers College, Columbia University, she organized a series of international drawing and cognition research symposia, in collaboration with colleagues from the U.K. She holds a B.A in Art and Cognition from Harvard University and a MFA in Painting from Yale, and an Ed.D from Columbia University in art education and cognitive studies. She teaches foundation drawing at Pratt Institute in Brooklyn, and art education at Tyler School of Art, Temple University. She worked for many years as a teaching artist in the New York City public schools and has been involved in multiple local and national arts in education research projects. Her own art work is represented by Kenise Barnes Fine Art.
One thought on “Thinking Space: Connecting Art & Math in the Museum”
Thanks for the great post. I appreciate the inclusion of links to research. The link to Jonathan Wai’s publication is incorrect (second paragraph, second link). The culprit is the “http://think/?” in front of the correct link. http://think/?http:/www.researchgate.net/profile/Jonathan_Wai/publication/228627975_Spatial_Ability_for_STEM_Domains_Aligning_Over_50_Years_of_Cumulative_Psychological_Knowledge_Solidifies_Its_Importance/links/02bfe5148a51ab16e4000000.pdf