Thinking Space: Connecting Art & Math in the Museum

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.

Our challenge:

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.

Logistics:

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.

teachers drawing Robert Morris’s
teachers drawing Robert Morris’s “Untitled (Battered Cubes)”

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.

teachers looking at the drawings on the floor
teachers looking at the drawings on the floor

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.

teachers' paper sculptures on display
teachers’ paper sculptures on display

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

mitchell2REBECCA 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.

kantrowitzANDREA 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. 

Plan, Implement, Evaluate: Leveraging All Staff for Program Development

Written by Mike Deetsch, Director of Education & Engagement, Toledo Museum of Art

Plan

In 2010 the Toledo Museum of Art (TMA) passed its 2015 Strategic Plan with an emphasis on the Museum’s Purpose: Art Education. One of the primary intentions behind the plan was to create a more relevant and sustainable Museum and at this point we adopted the Strategic Objective of Teaching Visual Literacy.  The thought process behind this, brought forward by the Museum’s director Brian Kennedy, was that the Museum would leverage great works of art in the collection to teach people to see better in our 21st century’s image-saturated society.  Since this time there have been a variety of visual literacy-specific initiatives developed by the Museum, including The Art of Seeing Art thinking routine, a docent training class highlighting visual perception, and the creation of a Visual Literacy website.

In November 2014 the Toledo Museum of Art hosted the 47th annual conference for the International Visual Literacy Association (IVLA).  As part of the preparation for this conference, in January 2014 the education department was charged with designing a professional development program that would train all Museum staff and volunteers on the theories and processes around visual literacy. With the conference imminent, we wanted to ensure that any staff or volunteer in the organization would feel comfortable talking about visual literacy with any of our attending guests.

Before my colleagues and I developed the curriculum, we needed to clarify TMA’s approach to teaching visual literacy and its associated concepts. Our goal was to make the content accessible to a wide audience.  It might go without stating, but not everyone on our staff has a background in art, art history, or art museums.  Keeping in mind that we were going to be training such a diverse audience (i.e. all museum departments as well as docents and other volunteers), our approach couldn’t be intimidating and had to be presented in a fun and engaging way.

We had been incorporating visual literacy concepts into programming in a number of ways since 2010, but those programs largely lived with the education department.  To be successful on this project, it was clear that it was essential to engage a variety of staff members outside of education in order for the concepts to “stick” and be embodied throughout the organization.  Aided by strong support from the director’s office, we pulled together a cross-departmental team of 14 staff, for three consecutive Tuesdays in February 2014, to brainstorm around visual literacy concepts.  This team consisted of staff from curatorial, education, library, marketing, visitor engagement, visitor services, and the director’s office.

Visual Literacy Content Meeting 021114

Our meetings took place in a white board room (three walls covered in white board paint) where we were able to discuss, brainstorm, and illustrate ideas.  While the participants were not always in agreement, we were able to use these meetings (about six hours total) to land on consensus for our key process which include:

  1. an easy to understand definition of visual literacy,
  2. the Elements of Art and Principles of Design as the foundational vocabulary,
  3. the Art of Seeing Art thinking routine, and
  4. the concepts of interpretation distilled into four visual languages.

During these sessions the group realized the value of aligning the TMA’s definition of visual literacy with textual literacy.  The comparison to textual literacy is important for two reasons: one, it makes an analogy that people are already familiar with and, two, it gives the Museum the opportunity to shift the discussion from literacy to language.  The latter shift was key because focus groups had been telling us that literacy implies there are people who are illiterate, while language implies level of fluency.  TMA’s definition of visual literacy is the ability to read, comprehend, and write visual language.  Reading visual language is about the process of seeing, comprehending visual language is about the interpretation of seeing, and writing visual language is about the action you take in response to what you have seen.

Implement

With the definition, process, and concepts in place my colleague Kate Blake, Manager of Curriculum, and I drafted the curriculum for the professional development.  From the outset of writing the curriculum we identified a few musts: the program needed to be multidisciplinary, meaning it wasn’t going to be art history-centric; it needed to be activity-based; and it had to be taught in the galleries.

As museum educators we know the value in using a variety of approaches to gallery learning, including group discussion, small group activities, drawing, and independent exploration.  Facilitating activities, opposed to discussion only, would afford us the chance to engage with a variety of learning styles and dabble into a bit of game mechanics.  By making the approach activity-based, we were able to engage our staff in the overall experience which proved to be useful in retaining the concepts  introduced.

Staff participating in Visual Literacy workshop activity.
Staff participating in Visual Literacy workshop activity.

As I mentioned earlier this training was offered to TMA staff and volunteers, in all approximately 300 individuals.  In the end we designed a curriculum of 12 contact hours which introduced the concepts surrounding Visual Literacy, spent time on close looking techniques, and gave special emphasis to the four visual languages.  Kate and I knew that 12 hours was a significant commitment for people to give over during the work week, so we also developed a variety of workshop formats to adjust to people’s schedules accordingly.  Initially each of these sessions was facilitated by full-time TMA education staff but gradually transitioned two of our more experienced docents into facilitators.  These docents, who were both former docent board presidents, had been working closely with staff on visual literacy programming since 2010.

One lesson the facilitators quickly discovered during the workshops was the importance of acknowledging expertise, at all levels, throughout the professional development.  There were content experts, such as curators, as well as other areas of expertise. For example our security staff, which spends more time in the galleries than anyone else on staff, was actively encouraged to contribute their opinions and perspectives.  The guards’ comments were often  the most insightful for their interpretations and their observations of visitor interactions with the collection.

Evaluation and Next Steps

As a means of reflection, we developed an evaluation tool that  allowed us to make real time adjustments. Specifically we measured the digestibility (of content) and overall enjoyment.  To do this, we created a series of online surveys to collect feedback at various touch points during the 12 hour workshop.  The curriculum was grouped into six modules and each module had its own evaluation.  While the evaluation was not a requirement for participation, we collected over 300 surveys.  The general response was positive, with most activities receiving a rating of 5 (out of 6) on a Likert scale. Open-ended questions provided constructive feedback that we were able to act on immediately, such as making a slight adjustment to our definition of visual literacy and dropping activities that did not resonate or were too complicated.

Staff feedback to Visual Literacy workshops.
Staff feedback to Visual Literacy workshops.

All told between April and October 2014, our team of eight facilitated 28 workshops, totaling 336 hours, for 300 staff and volunteers.  The entire experience, from design to facilitation, relied heavily on cross-departmental staff involvement, input, and engagement.  As a result we were able to design a clear and concise introductory visual literacy curriculum which we have been able to repurpose for a variety of audiences and in a multitude of formats since getting the staff involved.  Our staff and volunteers clearly understand TMA’s Purpose is Art Education and that we will achieve it by Teaching Visual Literacy now.

Having the opportunity to share and rely on expertise throughout the Museum proved invaluable throughout the entire process.  How many of you have the opportunity to cross collaborate on projects from start to finish?  If so, what does that look like?  And do you have the opportunity to prototype new ideas?  How can we build that into our practice? I’d love to hear your thoughts and experiences.

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About the Author

headshotMIKE DEETSCH: Emma Leah Bippus Director of Education and Engagement at the Toledo Museum of Art, Deetsch is a key member of the Museum’s executive team, leading educational and programming initiatives across the Museum. He is responsible for curriculum development for all audiences, outreach, exhibition interpretive material and management of the docent program as well as conceptualizing innovative public programming.  He oversees a strong, motivated education staff and a highly engaged TMA docent corps responsible for developing visual literacy initiatives and partnering to create opportunities for visual literacy education and awareness.  Prior to joining the TMA staff, Deetsch served as a senior museum educator at the Brooklyn Museum, the exhibition and programs director at the Lexington Art League, and the student programs manager at the Kentucky Historical Society. Deetsch received his master’s degree in art education from the Pratt Institute and a bachelor’s degree in art history from Hanover College. He was chosen in 2011 to participate in the Getty Leadership Institute’s “Museum Leaders: the Next Generation.”