The aim of thesis was to determine students' involvement in the adoption of concepts related to the parabola. In addition to the inclusion, in this paper we will consider another issue related to the teaching of mathematics, the problem of conceptual change. We examined the students' perception of the parabola as the curve, the ability to recognize the parabola, the identification of the tangent to the parabola, and the ability of description of the tangent to the parabola. Furthermore, we examined how students define asymptote, and do they know to determine whether the parabola has asymptote or not. We investigated the involvement of students in the processing of the content related to the concept of a parabola. We connected with the involvement of achievements in mathematics. Based on results of the survey we can see that students have high selfefficacy assessment, behavioral and cognitive involvement both in mathematics in general, and specifically, regarding to the subject of the curve of the second order and to understand the role of quality of students' involvement in learning mathematics. At the end of this paper we described the activities that cover the problem areas that may arise during the teaching process of the parabola.