Abstract

BELMONTE, José Luis  and  SIERRA, Modesto. Intuitive models and pattern of level development. Relime [online]. 2011, vol.14, n.2, pp.139-171. ISSN 2007-6819.

The concept of infinity is essential for understanding mathematical notions as a limit, continuity, derivative, integral, succession and series, among others. This paper studies the evolution of the concept of infinity from the last year of primary education (students aged between 11 and 12) to the first year of university education (students aged between 18 and 19 years old). A questionnaire designed in part on the basis of the existing bibliography in this field was taken by more than 2,000 students in order to identify the tacit models of infinity in their performance or in their expressions. During the analysis of answers, a new indicator was used, the pattern of level evolution (PEN) as a quantifying element which allows our results to be compared with those of other investigations. Together with models already identified in other studies, our paper found three new tacit intuitive models.

Keywords : Infinity; Intuitive model; Pattern of level development; Conceptual diagram; 11 to 19 years old students.