Teaching Crystal Symmetry Using "Old Time" Dances

Abstract:

Symmetry is one of the most difficult concepts for students to master in an introductory mineralogy course. The basic symmetry elements that define crystal structures (mirror planes, rotation axes, center of symmetry, translation) are exactly the same operations used in “old time” square and contra dances. A kinesthetic learning approach is used to teach symmetry operations by having student dancers move through a sequence of symmetrical dance moves. In this model, each student represents an atom in an assigned crystallographic site. According to the rules of symmetry, at the end of each symmetry operation all atoms must reoccupy these assigned sites or their equivalents. In a square set it is easy to demonstrate mirror planes and 2- and 4-fold rotation axes. Some square sets include a progression where dancers progress one position each time through the dance—a representation of a 4-fold screw axis. Contra dances are done in long lines with alternating males and females. There is a progression to a new couple each time through the dance representing translation symmetry. It is also possible to demonstrate a center of symmetry as dancer/atoms are positioned equidistant along a line through the center of the dance set. To extend the metaphor, a successfully completed dance is an ordered crystal, a dance with a few mistakes has crystal defects, if a set totally breaks down this is an amorphous glass, and if the dancers complete the dance but not in time to the beat of the music this can then be ascribed to kinetic effects. We developed a series of videos of square and contra dances in collaboration with the School of Film and Photography at Montana State University. Typically, each dance has 8 different dance forms, and these were filmed in sequence as instructional videos with annotations of symmetry elements superposed. We then filmed the complete dances with live music and dance calling. A supporting website (https://serc.carleton.edu/32771) provides introductory information and animations on symmetry elements, theory of kinesthetic learning, “old time” dance conventions, and the demonstration and live dance performance videos of two square dances, a contra dance, and a triplet dance. Embodied dance experiences emphasize the affective domain by lowering barriers to learning in a fun way that contributes to long-term learning.