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Recalibrating reference within a dual-space interaction environment

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Abstract

In this paper we examine how two groups of middle school students arrive at shared understandings of and solutions to mathematical problems. Our data consists of logs of student participation in the Virtual Math Teams (VMT) system as they work on math problems. The project supports interaction both through chat and through a virtual whiteboard. We have examined in detail, the sequential work these students do to constitute and specify ‘the problem’ on which they are working in the ways they produce whiteboard objects and text postings. Solutions emerge as students come to understand the problem on which they are working. This understanding is achieved through gradual respecification of the math problem on which they are working.

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Notes

  1. “Indexicals are sometimes defined simply as expressions that change their reference from one context to the next” (Nunberg 1993, p. 2).

  2. Transcripts of the text postings for Teams B and C are available in Appendix 1 and 2, respectively.

  3. Garfinkel et al. refer to these as “object[s]-of-sorts with neither demonstrable sense nor reference” (1981, p. 135).

References

  • Azevedo, F. S., diSessa, A. A., & Sherin, B. L. (2012). An evolving framework for describing student engagement in classroom activities. The Journal of Mathematical Behavior, 31, 270–289. doi:10.1016/j.jmathb.2011.12.003.

    Article  Google Scholar 

  • Beers, P. J., Boshuizen, H., Kirschner, P. A., & Gijselaers, W. H. (2005). Computer support for knowledge construction in collaborative learning environments. Computers in Human Behavior, 21, 623–643.

    Article  Google Scholar 

  • Cakır, M. P. (2009). How online small groups co-construct mathematical artifacts to do collaborative problem solving. (Doctoral dissertation, Drexel University). Retrieved from http://dspace.library.drexel.edu/bitstream/1860/3122/1/Cakir_Murat.pdf.

  • Cakir, M. P., Zemel, A., & Stahl, G. (2009). The joint organization of interaction within a multimodal CSCL medium. International Journal of Computer-Supported Collaborative Learning, 4, 115–149.

    Article  Google Scholar 

  • Danish, J. A., & Enyedy, N. (2007). Negotiated representational mediators: How young children decide what to include in their science representations. Science Education, 91, 1–35. doi:10.1002/(ISSN)1098-237X.

    Article  Google Scholar 

  • Danish, J. A., & Phelps, D. (2011). Representational practices by the numbers: How kindergarten and first?grade students create, evaluate, and modify their science representations. International Journal of Science Education, 33(15), 2069–2094. doi:10.1080/09500693.2010.525798.

    Article  Google Scholar 

  • diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition and Instruction, 22(3), 293–331. doi:10.1207/s1532690xci2203_2.

    Article  Google Scholar 

  • diSessa, A. A., & Sherin, B. L. (2000). Meta-representation: An introduction. The Journal of Mathematical Behavior, 19, 385–398

    Article  Google Scholar 

  • Fischer, F., & Mandl, H. (2005). Knowledge convergence in computer-supported collaborative learning: The role of external representation tools. The Journal of the Learning Sciences, 14, 405–441.

    Article  Google Scholar 

  • Garcia, A., & Jacobs, J. B. (1999). The eyes of the beholder: Understanding the turn-taking system in quasi-synchronous computer-mediated communication. Research on Language and Social Interaction, 32(4), 337–367.

    Article  Google Scholar 

  • Garfinkel, H. (1967). Studies in ethnomethodology. Cambridge: Polity Press.

    Google Scholar 

  • Garfinkel, H., & Sacks, H. (1970). On formal structures of practical actions. In J. C. McKinney & E. Tiryakian (Eds.), Theoretical sociology: Perspectives and developments (pp. 337–366). New York: Appleton-Century-Crofts.

  • Garfinkel, H., Lynch, M., & Livingston, E. (1981). The work of a discovering science constructed with materials from the optically discovered pulsar. Philosophy of the Social Sciences, 11(2), 131–158.

    Google Scholar 

  • Greiffenhagen, C. (2008). Unpacking tasks: The fusion of new technology with instructional work. Computer Supported Cooperative Work (CSCW), 17(1), 35–62. Retrieved from http://www.springerlink.com/index/N0760P8P725N2266.pdf.

    Article  Google Scholar 

  • Greiffenhagen, C., & Sharrock, W. (2005). Gestures in the blackboard work of mathematics instruction. Paper presented at the 2nd Conference of the International Society for Gesture Studies (Interacting Bodies), Lyon France. Retrieved from http://gesture-lyon2005.ens-lsh.fr/IMG/pdf/Greiffenhagen-Gesture.pdf

  • Hall, R. (1996). Representation as shared activity: Situated cognition and Dewey’s cartography of experience. Journal of the Learning Sciences, 5(3), 209–238.

    Article  Google Scholar 

  • Hanks, W. F. (1990). Referential practice: Language and lived space among the Maya. Chicago: University of Chicago Press.

    Google Scholar 

  • Hanks, W. F. (1992). The indexical ground of deictic reference. In A. Duranti & C. Goodwin (Eds.), Rethinking context: Language as an interactive phenomenon (Vol. 11, pp. 43–76). Cambridge: Cambridge University Press.

    Google Scholar 

  • Hanks, W. F. (1996). Language and communicative practices. Boulder: Westview.

    Google Scholar 

  • Hanks, W. F. (2000). Intertexts: Writings on language, utterance, and context. Lanham: Rowman & Littlefield.

    Google Scholar 

  • Hester, S., & Hester, S. (2010). Conversational actions and category relations: An analysis of a children’s argument. Discourse Studies, 12(1), 33–48. doi:10.1177/1461445609347233.

    Article  Google Scholar 

  • Hutchby, I. (2001). Conversation and technology: From the telephone to the internet. Cambridge: Polity Press.

    Google Scholar 

  • Kirschner, P. A., & Van Bruggen, J. (2004). Learning and understanding in virtual teams. CyberPsychology & Behavior, 7(2), 135–139.

    Article  Google Scholar 

  • Koschmann, T., & Zemel, A. (2009). Optical pulsars and black arrows: Discoveries as occasioned productions. Journal of the Learning Sciences, 18(2), 200–246.

    Article  Google Scholar 

  • Koschmann, T., & Zemel, A. (2011). “So that’s the ureter”. The informal logic of discovery work. Ethnographic Studies, 12, 34–46. Retrieved from http://www.socialsciences.manchester.ac.uk/disciplines/sociology/about/events/ethnography/journal/issue12/documents/koschmann-zemel.pdf.

    Google Scholar 

  • Livingston, E. (1986). The ethnomethodological foundations of mathematics. London: Routledge & Kegan Paul.

    Google Scholar 

  • Livingston, E. (1987). Making sense of ethnomethodology. London: Routledge & Kegan Paul.

    Google Scholar 

  • Livingston, E. (1999). Cultures of proving. Social Studies of Science, 29(6), 867–888.

    Article  Google Scholar 

  • Livingston, E. (2000). The availability of mathematics as an inspectable domain of practice through the use of origami. In S. Hester & D. Francis (Eds.), Local education order (pp. 245–270). Amsterdam: John Benjamins.

    Google Scholar 

  • Lonchamp, J. (2009). A three-level analysis of collaborative learning in dual-interaction spaces. International Journal of Computer-Supported Collaborative Learning, 4(3), 289–317. Retrieved from http://www.springerlink.com/index/c8344h6738426463.pdf.

    Article  Google Scholar 

  • Lonchamp, J. (2011). Deixis in synchronous CSCL systems. Proceedings from 3rd Conference on Computer Supported Education - CSEDU 2011.

  • Lynch, M. (1985). Discipline and the material form of images: An analysis of scientific visibility. Social Studies of Science, 15(1), 37.

    Article  Google Scholar 

  • Lynch, M. (1994). Representation is overrated: Some critical remarks about the use of the concept of representation in science studies. Configurations, 2(1), 137–149. Retrieved from http://www.petajwhite.net/Uni/910/Legit and Representation/Representation Precis/Lynch.doc.

    Article  Google Scholar 

  • Lynch, M. (2011). Credibility, evidence, and discovery: The case of the ivory-billed woodpecker. Ethnographic Studies, 12, 78–105.

    Google Scholar 

  • Macbeth, D. (2011). Understanding understanding as an instructional matter. Journal of Pragmatics, 43(2), 438–451. doi:10.1016/j.pragma.2008.12.006.

    Article  Google Scholar 

  • Medina, R., & Suthers, D. D. (2008). Bringing representational practice from log to light.

  • Mühlpfordt, M. (2006). Dual interaction Spaces: Integration Synchroner Kommunikation und Kooperation. 4. e-Learning Fachtagung Informatik.

  • Mühlpfordt, M., & Wessner, M. (2005). Explicit referencing in chat supports collaborative learning. In T. Koschmann, D. D. Suthers, & T.-W. Chan (Eds.), Computer supported collaborative learning: The next 10 years! (pp. 460–469). Mahwah: Erlbaum.

    Google Scholar 

  • Mühlpfordt, M., & Wessner, M. (2009). The integration of dual-interaction spaces. In G. Stahl (Ed.), Studying virtual math teams (pp. 281–293). New York: Springer.

  • Nunberg, G. (1993). Indexicality and deixis. Linguistics and Philosophy, 16(1–2), 1–43.

    Article  Google Scholar 

  • Parnafes, O. (2010). Representational practices in the activity of student-generated representations (SGR) for promoting conceptual understanding.

  • Psathas, G. (2007). Lebenswelt origins of the sciences. Hum Stud, 30(1), 1–2. doi:10.1007/s10746-007-9047-8.

    Article  Google Scholar 

  • Rochelle, J. (1996). Designing for cognitive communication: Epistemic fidelity or mediating collaborative inquiry. In D. L. Day & D. K. Kovacs (Eds.), Computers, communication and mental models (pp. 13–25). London: Taylor & Francis.

    Google Scholar 

  • Rochelle, J., & Teasley, S. D. (1995). The construction of shared knowledge in collaborative problem solving. In C. O’Malley (Ed.), Computer-supported collaborative learning, NATO ASO Series F: Computer and system sciences (Vol. 128) (pp. 69–97). Berlin: Springer.

    Chapter  Google Scholar 

  • Schegloff, E. (2000). On granularity. Annual Review of Sociology, 26, 715–720.

    Article  Google Scholar 

  • Schönfeldt, J., & Golato, A. (2003). Repair in chats: A conversation analytic approach. Research on Language and Social Interaction, 36(3), 241–284.

    Article  Google Scholar 

  • Sharrock, W., & Anderson, B. (2011). Discovering a practical impossibility: The internal configuration of a problem in mathematical reasoning. Ethnographic Studies, 12, 47–58.

    Google Scholar 

  • Stahl, G. (2009). Studying virtual math teams. New York: Springer.

    Book  Google Scholar 

  • Stahl, G., Zhou, N., & Toledo, R. (2006). The Virtual Math Teams project: A global math discourse community. Proceedings from International Conference on Computers and Education (ICCE ’06), Beijing, China. Retrieved from http://www.cis.drexel.edu/faculty/gerry/pub/icce2006.pdf

  • Suchman, L. A. (1988). Representing practice in cognitive science. Human Studies, 11(2), 305–325.

    Article  Google Scholar 

  • Suchman, L. A. (2006). Human–machine reconfigurations: Plans and situated actions (learning in doing: Social, cognitive and computational perspectives) (2nd ed.). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Suthers, D. D. (2005). Collaborative knowledge construction through shared representation. 38th Hawai’i International Conference on the System Sciences,.

  • Suthers, D., Girardeau, L., & Hundhausen, C. (2003). Deictic roles of external representations in face-to-face and online collaboration. Proceedings from International Conference on Computer Support for Collaborative Learning, Dordrecht, NL. Retrieved from http://metheny.ics.hawaii.edu/papers/2003/Suthers-et-al-CSCL2003.pdf

  • Van Bruggen, J. M., & Kirschner, P. A. (2003). Designing external representations to support solving wicked problems. In J. Andriessen, M. Baker, & D. Suthers (Eds.), Arguing to learn: Confronting cognitions in computer-supported collaborative learning environments (pp. 177―204). Dordrecht: Kluwer.

  • Van Bruggen, J. M., Kirschner, P. A., & Jochems, W. (2002). External representation of argumentation in CSCL and the management of cognitive load. Learning and Instruction, 12(1), 121–138.

    Article  Google Scholar 

  • van Drie, J., van Boxtel, C., Jaspers, J., & Kanselaar, G. (2005). Effects of representational guidance on domain specific reasoning in CSCL. Computers in Human Behavior, 21(4), 575–602. doi:10.1016/j.chb.2004.10.024.

    Article  Google Scholar 

  • Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. The Journal of Mathematical Behavior, 17(2), 167–181. Retrieved from http://www.sciencedirect.com/science/article/pii/S0364021399800573.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Woolgar, S. (1988). Time and documents in researcher interaction: Some ways of making out what is happening in experimental science. Human Studies, 11(2), 171–200.

    Article  Google Scholar 

  • Zemel, A., & Cakir, M. (2009). Reading’s Work in VMT. In G. Stahl (Ed.), Studying Virtual Math Teams (pp. 261–276). New York: Springer Publishing.

  • Zemel, A., Koschmann, T., LeBaron, C., & Feltovich, P. J. (2008). “What are we missing?” Usability’s indexical ground. Computer Supported Cooperative Work, 17, 63–85.

    Article  Google Scholar 

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Correspondence to Alan Zemel.

Appendices

Appendix 1

Table 1.

Table 1 Team B Chat log

Appendix 2

Table 2.

Table 2 Team C Chat log

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Zemel, A., Koschmann, T. Recalibrating reference within a dual-space interaction environment. Computer Supported Learning 8, 65–87 (2013). https://doi.org/10.1007/s11412-013-9164-5

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