Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki

Abstract

Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition of a measure, understood as a non-negative real function defined on a σ-field of sets of a space, is taught during the classes on mathematical analysis. It is observed that the concept of measurement causes great difficulties to students. This paper presents the results of research on students' difficulties in understanding and using the basic concepts of measure theory and integral. The research conducted in years 2006-2009 shed some light on the causes of those difficulties. The study involved students of the third year of the Mathematics Department at the Pedagogical University of Krakow.