caa a22 4500 445882158 CHVBK 20180317145547.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10649-010-9280-3 doi (NATIONALLICENCE)springer-10.1007/s10649-010-9280-3 Semiotic and theoretic control in argumentation and proof activities [Elektronische Daten] [Ferdinando Arzarello, Cristina Sabena] We present a model to analyze the students' activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin's structural description of arguments, Peirce's notions of sign, diagrammatic reasoning and abduction, and Habermas' model for rational behavior. Based on empirical qualitative analysis we identify three different kinds of semiotic actions featuring the organization of the argumentations, and related to different epistemological status of the arguments. In such semiotic actions, the students' argumentation and proof activities are managed and guided according to two intertwined modalities of control, which we call semiotic and theoretic control. The former refers to decisions concerning the selection and implementation of semiotic resources; the latter refers to decisions concerning the selection and implementation of a more or less explicit theory or parts of it. The structure of the model allows us to pinpoint a dialectical dynamics between the two. Springer Science+Business Media B.V., 2010 Argumentation nationallicence Proof nationallicence Semiotic control nationallicence Theoretic control nationallicence Abduction nationallicence Arzarello Ferdinando University of Torino, Torino, Italy aut Sabena Cristina University of Torino, Torino, Italy aut Educational Studies in Mathematics Springer Netherlands 77/2-3(2011-07-01), 189-206 0013-1954 77:2-3<189 2011 77 10649 https://doi.org/10.1007/s10649-010-9280-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10649-010-9280-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arzarello Ferdinando University of Torino, Torino, Italy aut NATIONALLICENCE 700 1- Sabena Cristina University of Torino, Torino, Italy aut NATIONALLICENCE 773 0- Educational Studies in Mathematics Springer Netherlands 77/2-3(2011-07-01), 189-206 0013-1954 77:2-3<189 2011 77 10649 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer