Choreographing Math

Visualization software and kinesthetic learning build understanding

Brandon Jones teaches math at a large, urban middle school. Three years ago the school adopted a school reform model that infuses the arts into the curriculum. Teachers took part in professional development activities that helped them understand how the arts can be used to teach across subject areas. After seeing an increase in learning when using this approach, Jones wanted to collaborate with colleagues on an interdisciplinary project to boost student learning.

Jones decided to incorporate a new activity into a unit on the geometry of polygons. He wanted students to be able to apply the concepts of angle measurements, understand regular and semi-regular polygons, and be able to show how polygons tessellate. He also wanted them to see how geometry connects to the real world. He knew his students would acquire a better understanding by physically modeling these concepts, and worked with the performing arts teacher to plan a three-day activity combining geometry with choreography.

Implementing Research-Based Strategies

Learners acquire and store knowledge in two primary ways: linguistic (by reading or hearing lectures), and nonlinguistic (through visual imagery, kinesthetic or whole-body modes, and so forth). While reading and lecture dominate in most classrooms, math offers an ideal setting for incorporating nonlinguistic learning experiences. Students can use manipulatives, models, graphs, and other tools to represent and apply the mathematical concepts described in textbooks.

• The more students use both systems of representing knowledge, the better they are able to think about and recall what they have learned. Helping students understand and represent knowledge nonlinguistically is the most underused instructional strategy (Marzano et al., 2001).


• Visual representations help students recognize how related topics connect (NCTM, 2000).


• Understanding of geometry increases when students learn to represent and visualize three-dimensional forms (Lehrer & Chazen, 1998).

Technology Supporting Success

Before starting the choreography activity, Jones reviewed key concepts: lines of symmetry, rotation, translation, reflection, and glide reflection. He used Geometer's Sketchpad, visualization software designed to support geometry learning, and a projector to model these concepts. Jones knew the company Web site provides online resources for educators, including a library of dynamic images.

Jones showed a graphic that demonstrated the concept visually (nonlinguistically) while he used words to explain the difference between a reflection and a glide reflection. Similarly, he used the software to show how to arrange polygons around a vertex to make repeating patterns, called tessellations.

Next, the performing arts teacher showed a video clip of a modern dance group. Stopping the video at key frames, he pointed out how the dancers arranged their bodies in angles that formed geometric shapes. Using the software and projection screen, Jones created polygons to represent the same dance movements. Students could look from the video screen to the projection screen to see two representations of the same shape—one version in three dimensions created by human forms, the other in two dimensions created by lines on a plane.

The students' next task: pair up to work on choreographing the concepts of rotation, translation, reflection, and glide reflection. They were told to imagine a line of symmetry between them. One student would strike a pose and the other would create the same pose in rotation or reflection. Once they could demonstrate these concepts, they choreographed movement tessellations with their own bodies. They first worked out each movement kinesthetically, then recorded the sequence of movements on paper, using geometric shapes. This connection between kinesthetic learning and graphic representation helped many students grasp the difference between a regular tessellation and a semi-regular tessellationoa concept that had previously challenged many of them. The arts teacher used a video camera to record each pair's movements.

As the final assessment Jones shared the videotape with the class. He asked students to write down when a good example of rotation, translation, reflection, or glide reflection and describe its qualities. It took two screenings of the video. Afterward, students switched papers with a neighbor and compared their descriptions. Green and his students realized how much the video supported their understanding once they had only words to use as descriptions. Students were now better able to recall and apply their understanding of these concepts, as well as having had a rich learning experience.