caa a22 4500 445345586 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10758-011-9181-2 doi (NATIONALLICENCE)springer-10.1007/s10758-011-9181-2 Development Process of a Praxeology for Supporting the Teaching of Proofs in a CAS Environment Based on Teachers' Experience in a Professional Development Course [Elektronische Daten] [Nurit Zehavi, Giora Mann] This paper presents the development process of a praxeology (theory-of-practice) for supporting the teaching of proofs in a CAS environment. The characteristics of the praxeology were elaborated within the frame of a professional development course for teaching analytic geometry with CAS. The theoretical framework draws on Chevallard's anthropological approach to the didactics of mathematics and Duval's analysis of transformations within and between registers of semiotic representations. The teachers (n=43) were asked (a) to draw conjectures regarding unfamiliar behavior of tangents to hyperbola, before and after exploration using given slider bars; and (b) to prove their conjectures after being exposed to the algebraic expressions underlying the slider bars. The teachers were also asked twice, before and after (b), to rate the need to ask students for an algebraic proof in similar tasks. Three types of proofs are presented in an increasing order of the level of mathematical maturity exhibited in each proof. Based on results coming from the empirical study, we propose a praxeology for preparing teachers to teach proofs consisting of Task design, Techniques, and Didactical discourse. Springer Science+Business Media B.V., 2011 Computer algebra systems nationallicence Proof nationallicence Analytic geometry nationallicence Praxeology nationallicence Semiotic representations nationallicence Slider bars nationallicence Zehavi Nurit Science Teaching Department, The Weizmann Institute of Science, 76100, Rehovot, Israel aut Mann Giora Beit Chanan, 76868, Rehovot, Israel aut Technology, Knowledge and Learning Springer Netherlands 16/2(2011-07-01), 153-181 2211-1662 16:2<153 2011 16 10758 https://doi.org/10.1007/s10758-011-9181-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10758-011-9181-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zehavi Nurit Science Teaching Department, The Weizmann Institute of Science, 76100, Rehovot, Israel aut NATIONALLICENCE 700 1- Mann Giora Beit Chanan, 76868, Rehovot, Israel aut NATIONALLICENCE 773 0- Technology, Knowledge and Learning Springer Netherlands 16/2(2011-07-01), 153-181 2211-1662 16:2<153 2011 16 10758 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer