Coordination of approximations in secondary school students’ understanding of the concept of limit

Abstract

The aim of this study was to characterize the role of the coordination of the approximation processes in the understanding of the notion of limit. Answers of 64 postsecondary school students to 7 problems reflecting dynamic and metric conceptions of limit notion were analyzed. The results indicate that the metric understanding of limit in terms of inequality supported the coordination of the approximations in the domain and the range when the lateral approximations coincide, though students were not capable of making this coordination when the lateral approximations do not coincide. This fact indicates the cognitive difference between the coordinate of the approximation in the domain with the approximation in the range either in the case that the lateral approximations coincide or not. This finding suggests that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.