Abstract
The article presents a report on four 45 minute sessions with a group of 17 year old humanities students. These sessions were the first of a series organised with the aim of exploring the possibilities of elaborating didactical situations that would help the students overcome epistemological obstacles related to limits. Students' attitudes pertinent to the development of the notion of limit, as well as changes of these attitudes, are described and analysed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Remark: The literature below contains, beside the direct references from the paper, also some articles and books which inspired me in the organisation of the sessions (Laborde, 1982), and in the interpretation of the students' attitudes (Balacheff, 1984; Bell, 1976; Fischbein, 1979; Davis, 1981; Tall, 1980).
BachelardG.: 1938, La formation de l'esprit scientifique, PUF, Paris.
Balacheff, N.: 1984, ‘Processus de preuve et situations de validation’, in Recueil des Textes et Comptes Rendus de la Illème Ecole d'Eté de Didactique des Mathématiques, Juillet, Orléans.
BellA. W.: 1976, A study of pupils' proof-explanations in mathematical situations’, Educational Studies in Mathematics 7, 23–40.
BourdieuP.: 1980, Le sens pratique, Eds de Minuit, Paris.
BrousseauG.: 1980, ‘Problèmes de l'enseignement des décimaux’, Recherches en Didactique des Mathématiques, 1.1, 11–58; 2.1, 37–127.
Brousseau, G.: 1986, Fondements et méthodes de la didactique des mathématiques, Thèse d'Etat, Université de Bordeaux, France.
Davis, P. J. and R. Hersh: 1981, The Mathematical Experience, Birkhäuser.
FischbeinE. et al.: 1979. ‘The intuition of infinity’, Educational Studies in Mathematics 10, 3–40.
HouzelC. et al.: 1976. Philosophie et calcul de l'infini, F. Maspero, Paris.
JuszkiewiczP.: 1976, History of Mathematics, Vol. III, Polish Scientific Publishers, Warsaw (in Polish).
Laborde, C.: 1982, ‘A propos d'une situation d'interaction et de communication en géométrie’, Document de travail pour le Colloque: “Nouvelle perspectives dans l'étude expérimentale du développement de l'intelligence”, Genève, 1982.
Lakatos, I.: 1978a, ‘Cauchy and the continuum”, in Mathematics, Science and Epistemology, The Philosophical Papers of Imre Lakatos, Cambridge University Press.
Lakatos, I.: 1978b, ‘The renaissance of empiricism in the recent philosophy of mathematics’, in Mathematics, Science and Epistemology, The Philosophical Papers of Imre Lakatos, Cambridge University Press.
Rucker, R.: 1982, Infinity and the Mind, the Science and the Philosophy of the Infinite, Birkhäuser.
Sierpińska, A.: 1985a, ‘Obstacles epistémologiques relatifs à la notion de limite’, Recherches en Didactique des Mathématiques, 6.1, 5–67.
Sierpińska, A.: 1985b, ‘La notion d'obstacle epistémologique dans l'enseignement des mathématiques’, Actes de la 37ème Rencontre CIEAEM, Leiden, 1985.
Tall D.: 1980, ‘The notion of infinite measuring number and its relevance to the intuition of infinity’, Educational Studies in Mathematics 11, 271–284.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sierpińska, A. Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics 18, 371–397 (1987). https://doi.org/10.1007/BF00240986
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00240986