TEACHING SYMMETRY USING KINESTHETIC LEARNING--AN EXERCISE USING "OLD TIME" DANCES

Symmetry is one of the most difficult concepts for students to master in an introductory mineralogy course. It is an abstract concept, and prior to this class students rarely have had any formal introduction to thinking in 3-D or about the relationships encompassed by symmetry that describe solid objects such as crystals. In a traditional unit on crystallography, topics such as basic symmetry elements (rotation axes, mirrors, center of symmetry), point group symmetry (permissible collections of symmetry elements), translation (including screw axes and glide planes), and lattices and unit cells are introduced as the architecture that defines the internal structure of minerals and their external crystal forms. In toto, these concepts present formidable barriers to learning (in the cognitive domain), and consequent fear of the subject as being too hard and arcane (in the affective domain). In response, we have developed a series of kinesthetic learning exercises (in the psycho-motor domain) to demonstrate symmetry operations in a fun and accessible way using "old time" square and contra dances. The same symmetry operations that define crystal structures are precisely the same operations that are used in "old time" dances. In this learning module, students experience symmetry operations by physically doing the movements of the symmetry operations. Each dancer "becomes" an atom in a crystal structure, and physically moves through space to the next positions prescribed by the symmetry operation. Symmetry elements emerge as the dance progresses, and if done successfully, dancers finish at specified locations forming a "perfectly ordered crystal. Web-based video clips were produced to a) demonstrate each individual dance move with symmetry defined, b) "live" demonstration videos of the called dances with music, and c) an audio tape of music and calling for instructors to use in their own in-class dances. After this introduction to symmetry, other approaches to teaching crystallography include Escher prints, ball-and-stick models, and Shape computer software. The video clips were made in collaboration with the graduate class in Film Preparation, Media and Theater Arts at Montana State University. The instructional module can be accessed at: http://serc.carleton.edu/32763. This project was funded by NSF DUE 06-18482.