N. ALBERTI, M. F. ANDRIANI, M. BEDULLI, S. DALLANOCE, R. FALCADE, S. FOGLIA, S. GREGORI,
L. GRUGNETTI, C. MARCHINI, F. MOLINARI, F. PEZZI, A. RIZZA and C. VALENTI
Sulle difficoltà di apprendimento del concetto di limite
In memoria di Francesco Speranza
Received: 14 Febbraio 2000
Mathematics Subject Classification (2000): 00A35 - ZDM D 70 - I 20
Abstract: Our work team has been carrying on, since some years, a re search about difficulties being related to the learning of the concept of limit. During CIEAEM 50 (1998) a com munication and a workshop (Grugnetti, Rizza & all. and Andriani, Dallanoce & all., 1999) were presented that illustrated the first step of our work: an enquiry that was aimed at answering the question "why?"Among, the numerous aspects, more or less well known, that are related to the learning of the concept, our work pointed out the importance of the linguistic aspect. The assumption that natural language affects or even hinders the understanding and the acceptance of the mathematical concept of limit was confirmed. In particular the "strong" idea of limit as barrier and the deriving negative connotation can represent a huge pre-existing obstacle to any didactic action. Such an idea, together with the well known epistemological difficulties,makes the teacher's intervention poorly effective. The examination of carried out enquiries has pointed out that in students the mastery of calculation techniques does not always coincide with an actual understanding of the concept. The answer of traditional teaching to the complexity of issues that are related to the concept of limit appears to be unsatisfactory. As a matter of fact the introduction of such a concept is confined to the last years of high school without any previous proper preparatory work. The teacher actually seems rather concerned with "keepingthe problem hidden" until it is formally dealt with than with having students intuitively and gradually familiarising themselves with limit-related concepts such as that of infinity, infinitesimal, and continuity by using the chances that even "elementary" mathematics can offer. Being convinced that these concepts are present at an intuitive level at all ages, our research was aimed on the one hand at making them come out and on the other at looking for strategies to strengthen them.