THE DIFFICULTIES AND REASONING OF UNDERGRADUATE MATHEMATICS STUDENTS IN THE IDENTIFICATION OF FUNCTIONS Theodossios ZACHARIADES* University of Athens Department of Mathematics e-mail: tzaharia@math.uoa.gr Constantinos CHRISTOU University of Cyprus Department of Education e-mail: edchrist@ucy.ac.cy Eleni PAPAGEORGIOU University of Cyprus Department of Education e-mail: edelpa@ucy.ac.cy ABSTRACT In this paper we investigated the difficulty levels of the identification of functions in different representations of mathematical relations. The relative difficulties associated with functions and developmental levels were examined through a written test administered to 38 first year undergraduate students. The results appear to support the assumption that there is a developmental pattern in students’ thinking in identifying functions from their symbolic and graphical forms. * The research presented in this paper was funded by the University of Athens (EËÊÅ). Part of the study was conducted during the academic year 2000-01, when the first author was a visiting professor at the Department of Mathematics and Statistics of the University of Cyprus.