Choreographing complexity: investigation of elementary preservice teachers' quantitative manipulation in large group formations

This study accumulated empirical evidence pertaining to preservice teachers' (n = 62) reasoning processes while choreographing group formations with embedded algebra tasks. The activities were designed to facilitate examination of the potential pedagogical connections between choreographing formation and mathematics, with particular emphasis on creating geometrical formation designs accompanied by corresponding algebraic equations. This study used a reflective thematic analysis to investigate the experiences and sense-making of participants during the choreography activity and related reflection. Analysis of the results revealed that the participants recognised and utilised a multiplicity of connections pertaining to the complexity of the formations and mathematical factors within the equations. This study verified that the participants were able to employ mathematical patterns of increasing levels of complexity to generate original and creative choreography designs for group formations, while completing embedded algebraic tasks. The strategies of developing choreographic positions employed by the participants revealed that mathematical models, especially those using a combination of algebra and geometry, can be useful for designing structural arrangements that are capable of flexibility and change.