caa a22 4500 44534556X CHVBK 20180317142827.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10758-011-9180-3 doi (NATIONALLICENCE)springer-10.1007/s10758-011-9180-3 Biza Irene Mathematics Education Centre, Loughborough University, LE11 3TU, Loughborough, UK aut Students' Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space [Elektronische Daten] [Irene Biza] In this paper I report a lengthy episode from a teaching experiment in which 15Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students' perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students' knowledge develops in specific social and cultural contexts, students' construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students' personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students' engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students' meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher. Springer Science+Business Media B.V., 2011 Tangent line nationallicence Mediation of meaning nationallicence Instructional example space nationallicence Dynamic Geometry software nationallicence Local straightness nationallicence Technology, Knowledge and Learning Springer Netherlands 16/2(2011-07-01), 125-151 2211-1662 16:2<125 2011 16 10758 https://doi.org/10.1007/s10758-011-9180-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10758-011-9180-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Biza Irene Mathematics Education Centre, Loughborough University, LE11 3TU, Loughborough, UK aut NATIONALLICENCE 773 0- Technology, Knowledge and Learning Springer Netherlands 16/2(2011-07-01), 125-151 2211-1662 16:2<125 2011 16 10758 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer