Concept of finite limit of a function at a point: meanings and specific terms

Abstract

In this paper, we present some results of an exploratory study performed with students aged 16-17. We investigate the different uses that these students make of terms such as ‘to approach’, ‘to tend’, ‘to reach’, ‘to exceed’ and ‘limit’ that describe the basic notions related to the concept of the finite limit of a function at a point. We use the interpretive framework of conceptual analysis to infer the meanings that students associate with these specific terms in connection with the effective use of terms in their answers.

Keywords:

• finite limit of a function at a point
• specific terms
• effective use of terms
• conceptions
• conceptual analysis
• non-compulsory secondary education

Acknowledgements

This study was performed with aid and financing from Fellowship FPU AP2010-0906 (MEC-FEDER), Projects EDU2009-11337 and EDU2012-33030 of the National Plan for R&D&R (MICIN), Subprogram EDUC and Group FQM-193 of the 3rd Andalusian Research Plan (PAIDI).

Notes

Non-Compulsory Secondary Education.

The expression ‘A limit describes how a function moves as x moves towards a certain point.’ is related to a dynamic conception of function, in which the graph is drawn in the axis of Cartesian coordinates, or the study of phenomena, such as the trajectory of a projectile.

Original answer: ‘Verdadero. Porque un límite es un punto al que una función se aproxima infinitamente sin llegar a él’.

Original answer: ‘Falso. Una función si puede sobrepasar un límite, ya que muchas veces para averiguar el límite se dan valores que dan lugar a números más altos’.

Original answer: ‘Falso. La función alcanza al límite, pero no puede sobrepasarlo’.

Original answer: ‘Falso. Un límite es un número aproximado al que se acerca una función sin resultado exacto’.

Original answer: ‘Falso. El límite no se puede alcanzar, pero sí aproximar y a partir de esas aproximaciones sacar el límite’.

Original answer: ‘Falso. Un límite es un tope numérico y no es aproximativo, sino concreto’.

Original answer: ‘Verdadero. La línea determinada por la función puede acercarse infinitamente pero nunca llegará, ej: 0.5; 0.05; 0.005; 0.0005’.