Reasoning based on the concept of finite limit of a function at a point

Abstract

This article analyses the students’ conceptions in Non-Compulsory Secondary Edu¬cation about the concept of finite limit of a function at a point from its graphical representation. Conceptions emerge from the arguments students express when applying their individual definitions to a selection of graphical models of the concept. The goodness of observed students’ argumentations is characterized in terms of three levels of coherence between single student’s arguments and his indi¬vidual definition previously developed. The results show conceptions recognized in previous studies. This study also detects particular conceptions, such as, necessity for image existence of a function at a point to discuss on its limit at that point. Likewise, we detect a balance between fully coherent argu¬ments and incoherent ones with the individual definition.