Abstract
Research has shown that the tools provided by dynamic geometry systems (DGSs) impact on students’ approach to Euclidean Geometry and specifically on investigating open problems asking for producing conjectures. Building on the work of Arzarello, Olivero, and other researchers, the study addresses the use of specific dragging modalities in the solution of conjecture problems. Within the frame of the theory of semiotic mediation (TSM), the investigation aims at describing the semiotic potential of the dragging tool: how personal meanings emerging from students’ activities in a DGS can potentially be transformed into mathematical meanings. A theoretical discussion is presented, concerning the possible meanings, emerging in respect to the different dragging modalities, their relationship with mathematical meanings concerning conjectures, and conditional statements. Further, it is described how meanings emerge during different exploratory processes and how they may be related to the basic components of a conditional statement: premise, conclusion, and conditional link between them. Some examples discussed are drawn from a teaching experiment where participants were introduced to certain ways of dragging and then interviewed while working on open problem activities.
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Notes
- 1.
Someone who mediates, i.e., a mediator; something that is mediated, i.e., a content/force/energy released by mediation; someone/something subjected to mediation, i.e., the “mediatee” to whom/which mediation makes some difference; the circumstances for mediation, viz, (a) the means of mediation, i.e., modality; (b) the location, i.e., site in which mediation might occur. For a full discussion, see Hasan (2002).
- 2.
Referring to the intentionality of the action, Baccaglini-Frank (2010) calls this kind of invariant the intentionally induced invariant. For the objective of this contribution, it is not necessary to introduce the terminology elaborated by Baccaglini-Frank.
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Acknowledgments
Special thanks to Anna Baccaglini-Frank for the thoughtful discussions that we had during the preparation of her dissertation and for sharing with me the rich set of data collected for her investigation.
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Mariotti, M. (2014). Transforming Images in a DGS: The Semiotic Potential of the Dragging Tool for Introducing the Notion of Conditional Statement. In: Rezat, S., Hattermann, M., Peter-Koop, A. (eds) Transformation - A Fundamental Idea of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3489-4_8
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