The ostensive dimension through the lenses of two didactic approaches

• Published in: ZDM Vol. 40; no. 2; pp. 179 - 188
• Main Authors: Arzarello, Ferdinando, Bosch, Marianna, Gascón, Josep, Sabena, Cristina
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2008; Springer Nature B.V
• Subjects: Classrooms; Dialectics; Didacticism; Education; Educational technology; Epistemology; Graphs; Learning; Learning Processes; Linguistic Theory; Mathematical analysis; Mathematical Concepts; Mathematics; Mathematics Activities; Mathematics Education; Original Article; Phenomenology; Semiotics; Society; Teaching; Teaching Methods; Mathematical Activity; Semiotic System; Didactic Contract; Semiotic Resource; Mathematical Practice
• ISSN: 1863-9690; 1863-9704
• DOI: 10.1007/s11858-008-0084-1

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.