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Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning

  • Lauren Vogelstein
  • Corey BradyEmail author
  • Rogers Hall
Original Article


We present exploratory analyses of three cases in which groups of four (quartets) worked with video recordings of choreographed performances from the opening ceremony of the 2016 Rio Olympic Games. We asked quartets to view the recordings, explain what performers were doing by reenacting what they noticed in the video, and create their own performances using props akin to those in the recording. In response, participants explored symmetries and transformations of quadrilaterals and triangles. We contribute to research on distributed, embodied mathematical learning at four levels. First, we argue for design research that engages in creative re-use by foraging in public media for performances with mathematical potential, then designing activities that invite learners to dissect and reenact these performances to explore that potential. Second, we analyze quartets’ work as a form of ensemble learning that hybridizes dance and mathematics. Third, we describe interactions that produced intercorporeality in the material work of quartets. Finally, we argue for reenactment as a supplement to methods of Interaction Analysis, using our own analysis as an illustration of this novel approach.


Foraging and dissection Dance and choreography Ensemble learning Embodied mathematics Interaction analysis methods 



We thank teachers and students who participated in this study; members of the Interaction Analysis Lab at Vanderbilt University; Quinley Brady, who made our enactment drawings; and Emma Reimers, who helped us clarify our photographic images with annotations. Vogelstein was supported as a Public Scholar by the Curb Center at Vanderbilt and in part by grants from the National Science Foundation (Division of Research on Learning in Formal and Informal Settings—1647242 and 1742257). Authors are listed in increasing order of seniority; each contributed equally.


  1. Abrahamson, D., & Lindgren, R. (2014). Embodiment and embodied design. The Cambridge Handbook of the Learning Sciences, 2, 358–376.CrossRefGoogle Scholar
  2. Bar, F., Weber, M. S., & Pisani, F. (2016). Mobile technology appropriation in a distant mirror: Baroquization, creolization, and cannibalism. New Media and Society, 18(4), 617–636.CrossRefGoogle Scholar
  3. Barron, B. (2003). When smart groups fail. The Journal of the Learning Sciences, 12(3), 307–359.CrossRefGoogle Scholar
  4. Brady, C., White, T., Davis, S., & Hegedus, S. (2013). SimCalc and the networked classroom. In The SimCalc vision and contributions (pp. 99–121). Dordrecht: Springer.CrossRefGoogle Scholar
  5. Cohen, E. G. (1994). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research, 64(1), 1–35.CrossRefGoogle Scholar
  6. Cohen, E. G., & Lotan, R. A. (1997). Working for equity in heterogeneous classrooms: Sociological theory in practice. New York: Teachers College Press.Google Scholar
  7. Eglash, R., Croissant, J. L., Di Chiro, G., & Fouche, R. (2004). Appropriating technology: Vernacular science and social power. Minneapolis: University of Minnesota Press.Google Scholar
  8. Erickson, F. (2004). Talk and social theory: Ecologies of speaking and listening in everyday life. Cambridge: Polity Press.Google Scholar
  9. Gerofsky, S. (2010). Mathematical learning and gesture: Character viewpoint and observer viewpoint in students’ gestured graphs of functions. Gesture, 10(2), 321–343.CrossRefGoogle Scholar
  10. Gerofsky, S. (2016). Approaches to embodied learning in mathematics. In L. D. English, & D. Kirsher (Eds.), Handbook of International Research in Mathematics Education (pp. 60–97). New York: Routledge.Google Scholar
  11. Goodwin, C. (2007). Participation, stance and affect in the organization of activities. Discourse and Society, 18(1), 53–73.CrossRefGoogle Scholar
  12. Goodwin, C. (2017). Co-operative action. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  13. Hahn, T., & Jordan, J. S. (2017). Sensible objects: Intercorporeality and enactive knowing through things. In C. Meyer, J. Streeck & J. S. Jordan (Eds.), Intercorporeality: Emerging socialities in interaction (pp. 267–288). New York: Oxford University Press.Google Scholar
  14. Hall, R., & Nemirovsky, R. (2012). Introduction to the special issue: Modalities of body engagement in mathematical activity and learning. Journal of the Learning Sciences, 21(2), 207–215.CrossRefGoogle Scholar
  15. Hall, R., Ma, J. Y., & Nemirovsky, R. (2014). Re-scaling bodies in/as representational instruments in GPS drawing. In V. Lee & M. Linn (Eds.), Technology and the body: Perspectives from the learning sciences (pp. 112–131). New York: Routledge.Google Scholar
  16. Hall, R., & Stevens, R. (2015). Interaction analysis approaches to knowledge in use. In A. A. diSessa, M. Levin & J. S. Brown (Eds.), Knowledge and interaction: A synthetic agenda for the learning sciences (pp. 72–108). New York: Routledge.Google Scholar
  17. Harss, M. (2016, August 8). For this choreographer, the Olympics are the zenith. New York Times. Retrieved from Accessed 4 Feb 2019.
  18. Headrick Taylor, K. (2017). Learning along lines: Locative literacies for reading and writing the city. Journal of the Learning Sciences, 26(4), 533–574.CrossRefGoogle Scholar
  19. Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. The Journal of the Learning Sciences, 4(1), 39–103.CrossRefGoogle Scholar
  20. Kahn, J., & Hall, R. (2016). Getting personal with big data: Stories with multivariable models about health and wealth. Paper presented at the annual meeting of the American Educational Research Association. Washington, D.C.Google Scholar
  21. Kendon, A. (1990). Conducting interaction: Patterns of behavior in focused encounters. New York: Cambridge University Press.Google Scholar
  22. Laurier, E. (2014). The graphic transcript: Poaching comic book grammar for inscribing the visual, spatial and temporal aspects of action. Geography Compass, 8(4), 235–248.CrossRefGoogle Scholar
  23. Lederman, W. (1957). Introduction to the theory of finite groups. Edinburgh: Oliver and Boyd.Google Scholar
  24. Lotan, R. A. (2003). Group-worthy tasks. Educational Leadership, 60(6), 72–75.Google Scholar
  25. Ma, J. Y., & Munter, C. (2014). The spatial production of learning opportunities in skateboard parks. Mind, Culture, and Activity, 21(3), 238–258.CrossRefGoogle Scholar
  26. Ma, J., & Hall, R. (2018). Learning a part together: Ensemble learning and infrastructure in a competitive high school marching band. Instructional Science 46(4), 507–532.CrossRefGoogle Scholar
  27. Ma, J. Y. (2017). Multi-party, whole-body interactions in mathematical activity. Cognition and Instruction, 35(2), 141–164.CrossRefGoogle Scholar
  28. Marin, A., & Bang, M. (2018). “Look it, this is how you know:” Family forest walks as a context for knowledge-building about the natural world. Cognition and Instruction, 36(2), 89–118.CrossRefGoogle Scholar
  29. Meyer, C., Streeck, J., & Jordan, J. S. (2017). Intercorporeality: Emerging socialities in interaction. New York: Oxford University Press.CrossRefGoogle Scholar
  30. Núñez, R., Edwards, L., & Matos, J. F. (2006). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1–3), 45–65.Google Scholar
  31. Rosling, H. (2006). The best stats you've ever seen [Video file]. Retrieved from
  32. Rowland, T. (1999). Pronouns in mathematics talk: Power, vagueness and generalisation. For the Learning of Mathematics, 19(2), 19–26.Google Scholar
  33. Shapiro, B. R., Hall, R., & Owens, D. A. (2017). Developing and using interaction geography in a museum. International Journal of Computer Supported Collaborative Learning, 12, 377–399.CrossRefGoogle Scholar
  34. Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: The murky and furtive world of mathematical inventiveness. ZDM—The International Journal on Mathematics Education, 45(2), 239–252.CrossRefGoogle Scholar
  35. Streeck, J., Goodwin, C., & LeBaron, C. (Eds.). (2011). Embodied interaction: Language and body in the material world. New York: Cambridge University Press.Google Scholar
  36. Teasley, S. D., & Roschelle, J. (1993). Constructing a joint problem space: The computer as a tool for sharing knowledge. In: S. P. Lajoie & S. J. Derry (Eds.), Computers as cognitive tools (pp. 229–258). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  37. Vogelstein, L., Brady, C., & Hall, R. (2017). Mathematical reflections: The design potential of ensemble performance. In P. Blikstein, & D. Abrahamson (Eds.), Proceedings of the 2017 conference on interaction design and children (pp. 583–588). New York: Association for Computing MachineryGoogle Scholar
  38. Webb, N. M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22(5), 366–389.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2019

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA

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