The concept of finite limit of a function at one point as explained by students of Non-Compulsory Secondary Education

Abstract

We review various educational studies of the mathematical concept of limit of a function at a point that indicate how colloquial uses of the terms “to approach,” “to tend toward,” “to reach,” “to exceed” and “limit” influence students’ conceptions of these terms. We then present the results of an exploratory study of this question performed with Spanish students in non-compulsory secondary education and analyze the responses they provide to justify the truth or falsity of statements related to the different characteristics of the concept of finite limit of a function at a point when they use these terms. Finally, we organize their answers according to the kinds of arguments made. Using the response profiles detected, we discuss the influence of everyday usage on the students’ arguments.