PME 34-2010 2- 241 EXPLORING THE NOTIONS OF COMPARISION, CONSERVATION AND MEASUREMENT OF THE AREA IN UNIVERSITY STUDENTS. A STUDY THROUGH THEIR ARGUMENTS Ma. Guadalupe Cabañas Sánchez and Ricardo Cantoral Uriza Institute for Research and Advanced Studies (Cinvestav) of the National Polytechnic Institute (IPN), México gcabanas.sanchez@gmail.com, rcantor@cinvestav.mx This contribution presents a study about how university students perceive that the area is compared, conserved and measured. The study is based on Toulmin’s argumentation scheme to reconstruct students’ arguments and analyze their mathematical logical reasons. The findings show that the students perceived: a) area conservation when they alluded both the parallelism relation and the elements of the formula to calculate the area of triangles or simulated movements on figures; b) area comparison when they became conscious on the relationship between the areas of the polygons and; c) area measurement when they managed to use the formula to calculate the area of the triangles or realized that the area had to be conserved. INTRODUCTION The study of the arguments produced by students and mathematicians has been the central theme of research in our discipline (Inglis, Mejía-Ramos & Simpson, 2007) and it is fundamentally supported in the discursive practices, through text analysis and the uses of the language. Arguing implies reasoning and it is shown through communication processes and social interaction. The interest for the study of arguments is justified in the mathematical validation processes, as well as in the construction of mathematical proofs (Fischbein, 1982; Recio & Godino, 2001; León & Calderón, 2001; Crespo & Farfán, 2005). Literature reports indicate that researches have been focused towards the analysis of types of arguments constructed by the students either to convince themselves or to persuade other people about the truth of a conjecture, through proof schemes (Harel & Sowder, 1998); to identify difficulties in the students in the construction of proofs (Weber, 2001); to comprise the role performed by the arguments as a validation resource in mathematical proofs (Crespo & Farfán, 2005); to study how mathematical notions are perceived (D’Amore & Maier 2003; Cabañas & Cantoral, 2006a, 2006b); or to describe forms of argumentation (Lavy, 2004; Inglis, Mejía-Ramos & Simpson, 2007). This contribution reports a study about how university students perceive that the area on plane regions –convex and non convex polygon– is compared, conserved and measured. The study is carried out through analysis of students’ arguments. This analysis is supported by the argumentation scheme proposed by Toulmin (1958).