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Supporting Students’ Productive Collaboration and Mathematics Learning in Online Environments

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STEM Education in the Junior Secondary

Abstract

Digital technologies provide a wide range of tools and functions that can support students’ learning of mathematics as well as the development of their mathematical and collaborative practices. Bringing such technologies to mathematics classrooms often do not parallel students’ previous classroom experiences, especially when collaborative practices are emphasized. When facilitating mathematics learning, discrepancies between students’ previous classroom experiences and their expected engagement with new collaborative technologies result in challenges to which teachers need to attend. In this chapter, we describe how a high school mathematics teacher engaged his students in an online collaborative environment, Virtual Math Team with GeoGebra (VMTwG), and how he addressed students’ technological and collaborative challenges to support growth in their geometrical understanding. From a cultural historical perspective, we present a model of how teachers can support students’ instrumentation of collaborative environments and mathematical understanding. In our model, during a mathematical activity, teachers progressively decentralize their role and, simultaneously, support students’ development and performance of collaborative practices. This model informs the theory of instrumental orchestration (Trouche L, Interact Comput 15(6):783–800, 2003; Trouche L, Int J Comput Math Learn 9(3):281–307, 2004; Trouche L, Instrumental genesis, individual and social aspects. The didactical challenge of symbolic calculators. Springer, New York, pp 197–230, 2005) by providing a pedagogical intervention trajectory that supports students’ instrumental genesis (Rabardel P, Beguin P, Theor Issues in Ergon Sci 6(5): 29–461, 2005) of collaborative mathematical environments and shifts students’ focus from their teacher to their peer collaborators.

This chapter is based upon work supported by the National Science Foundation (NSF), DRK-12 program, under award DRL-1118888. The findings and opinions reported are those of the authors and do not necessarily reflect the views of the funding agency.

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Notes

  1. 1.

    The project—Computer-Supported Math Discourse among Teachers and Students—is an NSF-funded collaboration among researchers affiliated with The Math Forum at the National Council of Teachers of Mathematics (NCTM) and Rutgers University-Newark.

  2. 2.

    The environment, Virtual Math Teams (VMT), has been the focus of years of development by a team led by Gerry Stahl, Drexel University, and Stephen Weimar, The Math Forum at the National Council of Teachers of Mathematics (NCTM) (formerly, The Math Forum @ Drexel University), and the target of considerable research (see, e.g., Powell & Lai, 2009; Stahl, 2008; Stahl, 2009b). This chapter is part of a recent body of investigations centered on an updated VMT with a multiuser version of GeoGebra (see, for instance, Alqahtani & Powell, 2016, 2017; Grisi-Dicker, Powell, Silverman, & Fetter, 2012; Powell, 2014; Powell, Grisi-Dicker, & Alqahtani, 2013; Stahl, 2013, 2015).

  3. 3.

    This and the next excerpt in this chapter are from students engaged in chat communication in VMTwG. In this setting, at the same time that they write informally, without focusing on conventions of academic writing, students direct their attention to communicating quickly their mathematical ideas to themselves and their teammates. For this reason, we have chosen not to correct their orthography or any other aspect of their writing. We feel that it is important to honor and understand their authentic expressions.

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Authors and Affiliations

  1. Rutgers University-Newark, Newark, NJ, USA

    Arthur B. Powell

  2. State University of New York, Cortland, NY, USA

    Muteb M. Alqahtani

  3. Burlington City High School, Burlington, NJ, USA

    Balvir Singh

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  1. Arthur B. Powell
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  3. Balvir Singh
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Correspondence to Arthur B. Powell .

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  1. University of Canberra, Bruce, Aust Capital Terr, Australia

    Robyn Jorgensen

  2. School of EPS, Griffith University, Brisbane, Queensland, Australia

    Kevin Larkin

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Powell, A.B., Alqahtani, M.M., Singh, B. (2018). Supporting Students’ Productive Collaboration and Mathematics Learning in Online Environments. In: Jorgensen, R., Larkin, K. (eds) STEM Education in the Junior Secondary. Springer, Singapore. https://doi.org/10.1007/978-981-10-5448-8_4

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