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Supporting students’ participation in authentic proof activities in computer supported collaborative learning (CSCL) environments

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Abstract

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this conception of proving: a particular learning perspective promoted in reform documents and a genre of computer tools, namely dynamic geometry software, which affords this perspective of learning within the context of mathematical proof. Tracing the move from absolutism to fallibilism in the philosophy of mathematics, I highlight the vital role of community in the production of mathematical knowledge. This leads me to an examination of a certain CSCL tool whose design is guided by knowledge-building pedagogy. I argue that knowledge building is a suitable pedagogical approach for the proof model presented in this paper. Furthermore, I suggest software modifications that will better support learners’ participation in authentic proof tasks.

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Notes

  1. Along with verification, these functions include explanation (providing insight into why a mathematical statement is true), discovery (the discovery or invention of new results), and communication (the negotiation of meaning), intellectual challenge (the self-realization/fulfillment derived from constructing a proof), and systematization (the organization of various results into a deductive system of axioms, concepts and theorems) (de Villiers 2003).

  2. The first generation was Computer Supported Intentional Learning Environments (CSILE).

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Acknowledgments

The author would like to thank Murat Çakır for his valuable comments on an earlier version of this manuscript.

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  1. Department of Computer Education and Educational Technology, Boğaziçi University, Bebek, 34342, Istanbul, Turkey

    Diler Öner

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Öner, D. Supporting students’ participation in authentic proof activities in computer supported collaborative learning (CSCL) environments. Computer Supported Learning 3, 343–359 (2008). https://doi.org/10.1007/s11412-008-9043-7

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