The ostensive dimension through the lenses of two didactic approaches - Arzarello, Ferdinando; Bosch, Marianna; Gascón, Josep; Sabena, Cristina (ZDM, 2008)
The paper presents how two different theories—the APC-space and the ATD—can frame in a complementary way the semiotic (or ostensive) dimension of mathematical activity in the way they approach teaching and learning phenomena. The two perspectives coincide in the same subject: the importance given to ostensive objects (gestures, discourses, written symbols, etc.) not only as signs but also as essential tools of mathematical practices. On the one hand, APC-space starts from a general semiotic analysis in terms of “semiotic bundles” that is to be integrated into a more specific epistemological analysis of mathematical activity. On the other hand, ATD proposes a general model of mathematical knowledge and practice in terms of “praxeologies” that has to include a more specific analysis of the role of ostensive objects in the development of mathematical activities in the classroom. The articulation of both theoretical perspectives is proposed as a contribution to the development of suitable frames for Networking Theories in mathematics education.