Resumen de Four conceptions of infinity

Magdalena Krátká, Peter Eisenman

• The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The aim of the research was to describe the development of students’ conceptions of infinity. These conceptions are built on the intuitive phenomenon of the horizon. We monitor the proportional representation of these conceptions in four combinations of views (into the distance and in depth) and contexts (arithmetical and geometrical).

  It can safely be maintained that the development of the proportional representation of the earliest conception comprehension of the concept of infinity, the so-called natural infinity, is not concurrent with the students’ age. The development of the proportional representation of the conception of actual infinity is non-decreasing, at least in the view into the distance, in both contexts with respect to age. In general, it can be stated that the proportional representation of individual conceptions of infinity is strongly dependent on both context and view.