How do mathematics textbooks address students misconceptions? The case of the tangent line

The study presented in this paper is a part of a substantive analysis of different didactical phenomena in relation to several mathematical concepts, conducted at the preparatory stage of a project aimed at investigating substantive and didactical competencies of pre-service teachers of mathematics. What I report here, relates to the exploration of didactical phenomena in relation to the tangent concept. Since school textbooks are the most common resource referred to by students and teachers, they deserve particular attention as one of the potential sources of concept images and mathematics-related beliefs of learners. In this article I present results from the analysis of ve, currently most popular, series of Polish secondary school mathematics textbooks. I attempt to answer the question of how the authors of these textbooks address a misconception known to be held by many students, namely that a line tangent to a curve has only one common point with that curve.