12th grade students’ understanding of limit and continuity of a function

Abstract

The concepts of limit and continuity of a function, which are fundamental for the study of Calculus in higher education, have been difficult to understand by the students. This calls for more research regarding the learning of these concepts in previous school years. This paper presents the results of a study aiming to analyze 12th grade students’ understanding of the limit and continuity concepts when solving tasks involving those concepts. The data were collected from the students’ written work in solving a set of tasks proposed in the classroom and an interview conducted with some students and were analyzed qualitatively and interpretatively using a theoretical framework involving three dimensions: meanings, representations and mathematical visualization, and learning difficulties. The results reveal that the participants in this study evidenced an instrumental understanding of the concepts of limit and continuity of a function. This understanding was initially of an intuitive nature, developed from experiences that are more close to their conceptions than from mathematical formalization. After the study of the concepts, the students’ understanding has a more formal nature, characterized by the application of rules and strategies pre-established by the mathematical conventions of the classroom.