Connecting levels of activity with classroom network technology

Article
  • 34 Downloads

Abstract

Classroom activity traditionally takes one of three forms, variously oriented toward the levels of individual students, small groups, or the whole class. CSCL systems, however, may enable novel ways to facilitate instruction within or sequence activity across these different levels. Drawing on theoretical accounts of learning at and across different scales of social interaction, this paper examines episodes of classroom activity featuring two learning environment designs that leverage networked digital devices to support face-to-face collaboration. Analysis of these episodes focused on two questions: When did activity shift between small and whole-group levels, and what mechanisms enabled or supported those shifts? Findings suggest that classroom activity in these environments was sometimes characterized by frequent, rapid shifts between levels, as well as instances that suggested hybrid forms of small-group and whole-class interaction. These shifts between and overlaps across levels were enabled and sustained through mechanisms including teacher orchestration, mediating roles played by virtual mathematical objects, learners’ appropriation of shared artifacts and resources, and emergent properties of these complex interactions among classroom participants.

Keywords

Mathematics Classroom networks Sociocultural theory Classroom orchestration 

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. DRL-0747536. Jeremy Roschelle and several anonymous reviewers provided insightful feedback on earlier drafts.

References

  1. Abrahamson, D., Trninic, D., Gutiérrez, J. F., Huth, J., & Lee, R. G. (2011). Hooks and shifts: A dialectical study of mediated discovery. Technology, Knowledge and Learning, 16(1), 55–85.Google Scholar
  2. Ares, N., Stroup, W. M., & Schademan, A. R. (2009). The power of mediating artifacts in group-level development of mathematical discourses. Cognition and Instruction, 27(1), 1–24.CrossRefGoogle Scholar
  3. Ball, D. (2000). Working on the inside: Using one’s own practice as a site for studying teaching and learning. In A. Kelly & R. Lesh (Eds.), Handbook of research Design in Mathematics and Science Education (pp. 365–402). New Jersey: Lawrence Erlbaum Associates.Google Scholar
  4. Brady, C., White, T., Davis, S., & Hegedus, S. (2013). SimCalc and the networked classroom. In S. Hegedus & J. Roschelle (Eds.), The SimCalc vision and contributions: Democratizing access to important mathematics (pp. 99–121). New York: Springer.CrossRefGoogle Scholar
  5. Carlsen, M. (2010). Appropriating geometric series as a cultural tool: A study of student collaborative learning. Educational Studies in Mathematics, 74(2), 95–116.CrossRefGoogle Scholar
  6. Chen, W., Looi, C. K., & Tan, S. (2010). What do students do in a F2F CSCL classroom? The optimization of multiple communications modes. Computers & Education, 55(3), 1159–1170.CrossRefGoogle Scholar
  7. Clark-Wilson, A. (2010). Emergent pedagogies and the changing role of the teacher in the TI-Nspire navigator-networked mathematics classroom. ZDM, 42(7), 747–761.CrossRefGoogle Scholar
  8. Cole, M. (1996). Cultural psychology: A once and future discipline. Cambridge: Harvard University Press.Google Scholar
  9. Colella, V. (2000). Participatory simulations: Building collaborative understanding through immersive dynamic modeling. The Journal of the Learning Sciences, 9(4), 471–500.CrossRefGoogle Scholar
  10. Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.CrossRefGoogle Scholar
  11. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3–4), 175–190.CrossRefGoogle Scholar
  12. Cress, U., & Kimmerle, J. (2008). A systemic and cognitive view on collaborative knowledge building with wikis. International Journal of Computer-Supported Collaborative Learning, 3(2), 105.Google Scholar
  13. Damsa, C. I., & Jornet, A. (2016). Revisiting learning in higher education—Framing notions redefined through an ecological perspective. Frontline Learning Research, 4(4), 39–47.CrossRefGoogle Scholar
  14. Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.CrossRefGoogle Scholar
  15. Derry, S. J., Pea, R. D., Barron, B., Engle, R. A., Erickson, F., Goldman, R., et al. (2010). Conducting video research in the learning sciences: Guidance on selection, analysis, technology, and ethics. The Journal of the Learning Sciences, 19(1), 3–53.CrossRefGoogle Scholar
  16. Dillenbourg, P. (2012). Design for classroom orchestration. Computers & Education, 69, 485–492.CrossRefGoogle Scholar
  17. Dillenbourg, P. (2015). Orchestration graphs: Modeling scalable education. Lausanne: EPFL Press.Google Scholar
  18. Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.CrossRefGoogle Scholar
  19. Enyedy, N. (2005). Inventing mapping: Creating cultural forms to solve collective problems. Cognition and Instruction, 23(4), 427–466.CrossRefGoogle Scholar
  20. Furberg, A., Kluge, A., & Ludvigsen, S. (2013). Student sensemaking with science diagrams in a computer-based setting. International Journal of Computer-Supported Collaborative Learning, 8(1), 41–64.CrossRefGoogle Scholar
  21. Guin, D., & Trouche, L. (1998). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.CrossRefGoogle Scholar
  22. Hegedus, S., & Kaput, J. (2004). An introduction to the profound potential of connected algebra activities: Issues of representation, engagement and pedagogy. Proceedings of the 28th conference of the International Group for the Psychology of mathematics education, 3, 129–136.Google Scholar
  23. Hegedus, S. J., & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM Mathematics Education, 41, 399–412.CrossRefGoogle Scholar
  24. Hegedus, S., & Penuel, W. (2008). Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68, 171–183.CrossRefGoogle Scholar
  25. Higgins, S. E., Mercier, E., Burd, E., & Hatch, A. (2011). Multi-touch tables and the relationship with collaborative classroom pedagogies: A synthetic review. International Journal of Computer-Supported Collaborative Learning, 6(4), 515–538.CrossRefGoogle Scholar
  26. Hunsu, N. J., Adesope, O., & Bayly, D. J. (2016). A meta-analysis of the effects of audience response systems (clicker-based technologies) on cognition and affect. Computers & Education, 94, 102–119.CrossRefGoogle Scholar
  27. Johnson, S. B. (2001). Emergence. The Connected Lives of Ants, Brains, Cities and Software. The Penguin: Allen lane.Google Scholar
  28. Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. The Journal of the Learning Sciences, 4(1), 39–103.CrossRefGoogle Scholar
  29. Kaput, J. (2000). Implications of the shift from isolated, expensive technology to connected, inexpensive, diverse and ubiquitous technologies. In M. O. J. Thomas (Ed.), Proceedings of the TIME 2000: An international conference on Technology in Mathematics Education (pp. 1–24). Auckland: The University of Auckland and the Auckland University of Technology.Google Scholar
  30. Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York: McMillan & National Council of Teachers of Mathematics.Google Scholar
  31. Klopfer, E., Yoon, S., & Perry, J. (2005). Using palm technology in participatory simulations of complex systems: A new take on ubiquitous and accessible mobile computing. Journal of Science Education and Technology, 14(3), 285–297.CrossRefGoogle Scholar
  32. Koschmann, T. D. (Ed.). (1996). CSCL, theory and practice of an emerging paradigm. Routledge.Google Scholar
  33. Lai, K., & White, T. (2014). How groups cooperate in a networked geometry learning environment. Instructional Science, 42(4), 615–637.CrossRefGoogle Scholar
  34. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  35. Leinhardt, G., Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.CrossRefGoogle Scholar
  36. Levy, S. T., & Wilensky, U. (2008). Inventing a “mid level” to make ends meet: Reasoning between the levels of complexity. Cognition and Instruction, 26(1), 1–47.CrossRefGoogle Scholar
  37. Linchevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations. Educational Studies in Mathematics, 30(1), 39–65.CrossRefGoogle Scholar
  38. Ludvigsen, S., & Arnseth, H. C. (2017). Computer-supported collaborative learning. In E. Duval, M. Sharples, & R. Sutherland (Eds.), Technology enhanced learning (pp. 47–58). Chicago: Springer International Publishing.CrossRefGoogle Scholar
  39. Mariotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1), 25–53.CrossRefGoogle Scholar
  40. Mehan, H. (1979). Learning lessons. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  41. Moschkovich, J. N. (2004). Appropriating mathematical practices: A case study of learning to use and explore functions through interaction with a tutor. Educational Studies in Mathematics, 55(1–3), 49–80.CrossRefGoogle Scholar
  42. Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42(3), 237–268.CrossRefGoogle Scholar
  43. Radford, L. (2013). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2(1), 7–44.Google Scholar
  44. Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. Oxford: Oxford University Press.Google Scholar
  45. Rogoff, B. (1995). Observing sociocultural activity on three planes: Participatory appropriation, guided participation, and apprenticeship. In J. V. Wertsch, P. del Rio, & A. Alvarez (Eds.), Sociocultural studies of mind (pp. 139–164). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  46. Roschelle, J., Dimitriadis, Y., & Hoppe, U. (2013). Classroom orchestration: Synthesis. Computers & Education, 69, 523–526.CrossRefGoogle Scholar
  47. Roschelle, J., & Pea, R. (2002). A walk on the WILD side: How wireless hand-helds may change CSCL. In G. Stahl (Ed.), Proceedings of the CSCL (Computer Supported Collaborative Learning) 2002. Boulder, CO, January, 7–11 2002. Hillsdale: Erlbaum.Google Scholar
  48. Roschelle, J., Penuel, W. R., & Abrahamson, L. A. (2004). The networked classroom. Educational Leadership, 61(5), 50–54.Google Scholar
  49. Roschelle, J., Tatar, D., Chaudhury, S. R., Dimitriadis, Y., Patton, C., & DiGiano, C. (2007). Ink, improvisation, and interactive engagement: Learning with tablets. IEEE Computer, 40(9), 42–48.CrossRefGoogle Scholar
  50. Säljö, R. (2010). Digital tools and challenges to institutional traditions of learning: Technologies, social memory and the performative nature of learning. Journal of Computer Assisted Learning, 26(1), 53–64.CrossRefGoogle Scholar
  51. Sawyer, R. K. (2005). Social emergence: Societies as complex systems. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  52. Saxe, G. B. (2002). Children's developing mathematics in collective practices: A framework for analysis. Journal of the Learning Sciences, 11(2–3), 275–300.CrossRefGoogle Scholar
  53. Schegloff, E., Jefferson, G., & Sacks, H. (1977). The preference for self-correction in the Organization of Repair in conversation. Language, 53(2), 361–382.CrossRefGoogle Scholar
  54. Schoenfeld, Smith, & Arcavi. (1993). Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55–175). Earlbaum: Hillsdale.Google Scholar
  55. Schwarz, B. B., De Groot, R., Mavrikis, M., & Dragon, T. (2015). Learning to learn together with CSCL tools. International Journal of Computer-Supported Collaborative Learning, 10(3), 239–271.CrossRefGoogle Scholar
  56. Stahl, G. (2006). Group cognition: Computer support for building collaborative knowledge (acting with technology).Google Scholar
  57. Stahl, G. (2009). Studying virtual math teams. New York: Springer. Computer-supported collaborative learning series #11.Google Scholar
  58. Stahl, G. (2012). Traversing planes of learning. International Journal of Computer-Supported Collaborative Learning, 7(4), 467–473.CrossRefGoogle Scholar
  59. Stahl, G. (2013). Learning across levels. International Journal of Computer-Supported Collaborative Learning, 8(1), 1–12.CrossRefGoogle Scholar
  60. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.CrossRefGoogle Scholar
  61. Stroup, W., Ares, N., & Hurford, A. (2005). A dialectic analysis of generativity: Issues of network-supported design in mathematics and science. Mathematical Thinking and Learning, 7(3), 181–206.CrossRefGoogle Scholar
  62. Stroup, W., Ares, N., Hurford, A. & Lesh, R. (2007). Diversity-by-design: The what, why, and how of generativity in next-generation classroom networks. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the Future in Mathematics Education (pp. 367–394). Routledge.Google Scholar
  63. Sutherland, S. M., & White, T. F. (2016). Constraint-referenced analytics of algebra learning. Journal of Learning Analytics, 3(3), 143–169.CrossRefGoogle Scholar
  64. Szewkis, E., Nussbaum, M., Rosen, T., Abalos, J., Denardin, F., Caballero, D., et al. (2011). Collaboration within large groups in the classroom. International Journal of Computer-Supported Collaborative Learning, 6(4), 561–575.CrossRefGoogle Scholar
  65. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  66. Wertsch, J. (1985). Vygotsky and the social formation of mind. Cambridge: Harvard University Press.Google Scholar
  67. White, T. (2006). Code talk: Student discourse and participation with networked handhelds. International Journal of Computer-Supported Collaborative Learning, 1(3), 359–382.CrossRefGoogle Scholar
  68. White, T., & Pea, R. (2011). Distributed by design: On the promises and pitfalls of collaborative learning with multiple representations. Journal of the Learning Sciences, 20(3), 489–547.CrossRefGoogle Scholar
  69. White, T., Sutherland, S., & Lai, K. (2010). Constructing Collective Algebraic Objects in a Classroom Network. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the Thirty Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1523–1530). Columbus: The Ohio State University.Google Scholar
  70. White, T., Wallace, M., & Lai, K. (2012). Graphing in groups: Learning about lines in a collaborative classroom network environment. Mathematical Thinking and Learning, 14(2), 149–172.CrossRefGoogle Scholar
  71. Wilensky, U., & Stroup, W. (1999a). Learning through participatory simulations: Network-based design for systems learning in classrooms. In C. Hoadley & J. Roschelle (Eds.), Proceedings of the conference on computer-supported collaborative learning (pp. 667–676). Mahwah: Erlbaum.Google Scholar
  72. Wilensky, U. & Stroup, W. (1999b). HubNet. http://ccl.northwestern.edu/netlogo/hubnet.html. Center for Connected Learning and Computer-Based Modeling. Evanston: Northwestern University.
  73. Wilensky, U. 1999. NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling. Evanston: Northwestern University.
  74. Zurita, G., & Nussbaum, M. (2004). Computer supported collaborative learning using wirelessly interconnected handheld computers. Computers & Education, 42, 289–314.CrossRefGoogle Scholar

Copyright information

© International Society of the Learning Sciences, Inc. 2018

Authors and Affiliations

  1. 1.School of EducationUniversity of California, DavisDavisUSA

Personalised recommendations