Curricular possibilities of graphic interpolation/extrapolation in secondary school

Abstract

In this paper, we present an empirical study on Interpolation/Extrapolation (I/E) with students of the Social Sciences Bachelor of Science (16-17 years). We have designed a set of function templates and analyzed: 1) their curricular possibilities, 2) the difficulties of the students in the realization of graphic I/E, and 3) their preference for the graphical method over the algebraic one. The adopted methodology, of qualitative type, has been Action research, consisting of 5 cycles, with a total of 83 students. The instruments used for the analysis of the results have been: students’ productions, two tests (Likert scale and open questions) and a time control table. These have allowed us to conclude that: 1) the set of function templates designed is a representation system and the use of graphic templates provides a good resource to identify the families of functions; 2) students have few difficulties in solving graphical I/E tasks, some of them associated with the location of points in the plane and the use of rules of three; and 3) the graphical method is more motivating than algebraic, preferring its use in most I/E tasks and implying that students should spend more time studying mathematics with the graphical method than with the algebraic method.