Abstract
This paper is about orchestrating the emergence of conceptual learning in a collaborative setting. We elaborate on the idea of critical moments in group learning, events which may lead to a particular development at the epistemic level regarding the shared object. We conjecture that teachers’ identification of critical moments may help them guide students to the emergence of conceptual learning. The complexity of small group settings in classrooms prevents teachers from noticing these critical moments, though. Here we present an environment, SAGLET (System for Advancing Group Learning in Educational Technologies), based on the VMT (Virtual Math Teams) environment (Stahl 2009), which allows teachers to observe multiple groups engaging in problem-solving in geometry. SAGLET capitalizes on machine learning techniques to inform teachers about on-line critical moments by sending them alerts, so that they can then decide whether (and how) to use the alerts in guiding their students. One teacher in an elementary school used SAGLET to help multiple groups of students solve difficult problems in geometry. We observed how the teacher mediated two cohorts of multiple groups at two different times in a mathematics classroom. We show that in both cases the teacher could detect the needs of the groups (partly thanks to the alerts) and could provide adaptive guidance for all the groups.
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Notes
Schwarz and Asterhan used the term ‘moderation’ to indicate that guidance is caring and at the same time non-intrusive. While Schwarz and Asterhan did not use the term ‘orchestration’, a posteriori, moderation can be considered as a type of orchestration.
We are aware of the controversy about the relations among time-on-task, engagement and learning. Our approach is practical, as we claim that teachers should know about moments when their students are not engaging in the task at hand, so that they can decide whether or not to intervene.
References
Asterhan, C. S. C., & Schwarz, B. B. (2016). Argumentation for learning: Well-trodden paths and unexplored territories. Educational Psychologist, 51(2), 164–187.
Baker, R. S., & Inventado, P. S. (2014). Educational data mining and learning analytics. In J. A. Larusson & B. White (Eds.), Learning Analytics: From Research to Practice (pp. 61–75) Springer New York.
Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10(1–2), 113–164.
Cuendet, S., Dehler-Zufferey, J., Ortoleva, G., & Dillenbourg, P. (2015). An integrated way of using a tangible user interface in a classroom. International Journal of Computer-Supported Collaborative Learning, 10, 183–208.
D’Mello, S., Lehman, B., Pekrun, R., & Graesser, A. (2014). Confusion can be beneficial for learning. Learning and Instruction, 29, 153–170.
Damşa, C. I. (2014). The multi-layered nature of small-group learning: Productive interactions in object-oriented collaboration. International Journal of Computer-Supported Collaborative Learning. https://doi.org/10.1007/s11412-014-9193-8.
Damşa, C., & Ludvigsen, S. (2016). Learning through interaction and the co-construction of knowledge objects in teacher education. Culture and Social Interaction: Learning.
De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11–18.
Dillenbourg, P. (2013). Design for Classroom Orchestration. Computers & Education, 69, 485–492.
Eisenhardt, K. M. (1989). Building theories from case study research. The Academy of Management Review, 14(4), 532–550.
Eisenhardt, K. M., & Graebner, M. E. (2007). Theory building from cases: Opportunities and challenges. The Academy of Management Journal, 50(1), 25–32.
Erez, M., & Yerushalmy, M. (2006). “If you can turn a rectangle into a square, you can turn a square into a rectangle”: Young students’ experience the dragging tool. The International Journal of Computers for Mathematical Learning, 11(3), 271–299.
Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1&2), 3–20.
Hakkarainen, K. (2010). Learning communities in the classroom. In K. Littleton, C. Wood, and J. Kleine Staarman (Eds). International Handbook of Psychology in Education (pp. 177–225). Emerald Group Publishing.
Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher and J. Kilpatrick (Eds.), Mathematics and Cognition (pp. 70–95). Cambridge University Press.
Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44, 55–85.
Lemke, J. (1990). Talking Science: Language, Learning and Values. Norwood, NJ: Ablex.
Ludvigsen, S. R. (2009). Sociogenesis and cognition. The struggle between social and cognitive activities. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 302–317). New York: Routledge.
MacDonald, B., & Walker, R. (1977). Case Study and the Social Philosophy of Educational Research. In D. Hamilton and others (eds.), Beyond the numbers Game. London: Macmillan Education.
Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass Publication.
Michaels, S., O’Connor, C., & Resnick, L. B. (2008). Deliberative discourse idealized and realized: Accountable talk in the classroom and in civic life. Studies in Philosophy and Education, 27, 283–297.
Monteil, J-.M. (1989). Eduquer et former. Grenoble. Presses Universitaires de Grenoble.
Romero, M. (2010). Gestion du temps dans les Activités Projet Médiatisées à Distance (thèse de Doctorat en cotutelle européenne). Université de Toulouse (CLLE-LTC UMR CNRS 5263) et Universitat Autònoma de Barcelona (SINTE SGR 2009 134).
Schwarz, B. B., & Asterhan, C. S. C. (2011). E-moderation of synchronous discussions in educational settings: A nascent practice. The Journal of the Learning Sciences, 20(3), 395–442.
Schwarz, B. B. & Baker, M. J. (2016). Dialogue, Argumentation and Education: History, Theory and Practice. Cambridge University Press.
Segal, A., Hindi, S., Prusak, N., Swidan, O., Livni, A., Palatnic, A., Schwarz, B. B., & Gal, K. (2017). Keeping the teacher in the loop: Technologies for Monitoring Group Learning in real-time. In International Conference on Artificial Intelligence in Education (pp. 64-76). Cham: Springer.
Stahl, G. (2009). Studying virtual math teams. Springer New York Dordrecht Heidelberg London.
Stahl, G., Koschmann T., Suthers D. (2006). Computer-supported collaborative learning: An historical perspective. In R. K. Sawyer (Ed.), Cambridge handbook of the learning Sciences (pp. 409–426). Cambridge, UK: Cambridge University Press.
Van Gog, T., Kester, L., Nievelstein, F., Giesbers, B., & Paas, F. (2009). Uncovering cognitive processes: Different techniques that can contribute to cognitive load research and instruction. Computers in Human Behavior, 25, 325–331.
Van Hiele, P. M., (1986). Structure and insight. A theory of Mathematics Education. Academic Press Inc.
Van Leeuwen, A. (2015). Learning analytics to support teachers during synchronous CSCL: Balancing between overview and overload. Journal of Learning Analytics, 2, 138–162.
Van Leeuwen, A., & Rummel, N. (2017). Teacher regulation of collaborative learning: research directions for learning analytics dashboards. In: Proceedings of the 12th international conference on Computer-supported Collaborative Learning (CSCL) 2017, Volume 1, pp 805–806.
Webster, L., & Mertova, P. (2007). Using narrative inquiry as a research method: An introduction to using critical event narrative analysis in research on learning and teaching. New York: Routledge.
Wise, A. F., & Vytasek, J. (2017). Learning analytics implementation design. In C. Lang, G. Siemens, A. F. Wise, & D. Gasevic (Eds.), Handbook of Learning Analytics (pp. 151–160). Society for Learning Analytics Research.
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21, 423–440.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation and autonomy in mathematics. Journal of Research in Mathematics Education, 27, 458–477.
Yin, R. K. (1994). Case Study Research: Design and Methods. (2nd ed.) thousand oaks, California. Sage.
Zufferey, G., Jermann, P., Lucchi, A., & Dillenbourg, P. (2009). TinkerSheets: using paper forms to control and visualize tangible simulations. In Proceedings of the 3rd international conference on tangible and embedded interaction (Cambridge, UK, Feb, 16-18, 2009). TEI ’09 (pp. 377–384). New York, NY: ACM.
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Schwarz, B.B., Prusak, N., Swidan, O. et al. Orchestrating the emergence of conceptual learning: a case study in a geometry class. Intern. J. Comput.-Support. Collab. Learn 13, 189–211 (2018). https://doi.org/10.1007/s11412-018-9276-z
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DOI: https://doi.org/10.1007/s11412-018-9276-z