BIZA, I., 2011. Students’ evolving meaning about tangent line with the mediation of a dynamic geometry environment and an instructional example space. Technology, Knowledge and Learning, 16 (2), pp.125-151.
In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 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.