Models of students’ conceptions about the tangent line

The results presented in this paper are a part of a doctoral study nearing completion which focuses on students’ conceptions about tangent lines. The study explores the ways in which students who have studied tangents in school in different contexts (Euclidean Geometry, Analytic Geometry and Analysis): (i) perceive properties that are not generally valid as defining conditions of the concept and (ii) create new, often not-valid, properties out of the fusion of information from across the different contexts. Data was collected through a questionnaire administered to 182 first year mathematics undergraduates in Greece at the very beginning of their studies. Here I exemplify from the data analysis in the course of which several models of the tangent line have emerged based on the above properties.