[1] For references about the Italian system of education see: Barra, M., Ferrari, M., Furinghetti, F., Malara, N. A. and Speranza, F. (editors): 1992, Italian research in mathematics education: common roots and present trends, Quaderno TID - CNR, serie FMI, n.12. Further information can be found in Bernardi, C. and Arzarello, F. (eds.): 1996, Educational System and Teacher Training in Italy, UMI-CIIM, Roma.

[2] Furinghetti, F.: (to appear), `Les mathématiques à l'école supérieure en Italie: une réforme par siècle', in Les sciences au lycée, un circle de réformes des mathématiques et de la physique en France et à l'étranger .

[3] Schubring, G.: 1987, `The cross-cultural `transmission' of concepts - The first international mathematical curricular reform around 1900, with an appendix on the biography of F. Klein', Occasional paper n. 92, corr. version February 1989.

[4] Besso, D.: 1869, `Del concetto di funzione nell'insegnamento della geometria elementare', Giornale di matematiche, 7, 131-136.

[5] Giovanni Gentile was the neo-idealist philosopher who, as Minister of Education under the Fascist regime, promoted the most important educational reform of the century about the school system in Italy.

[6] Secondary school in Italy is attended by students from 14 to 19 years of age, and is generally organized in a biennium followed by a triennium (see footnote 1).

[7] Note that in Italy - even up to the first year basic mathematical courses for sciences faculties - no essential distinction is made between `calculus' and `analysis'. This gives one more proof of the preference for the theoretical formal approach to the subject.

[8] This examination, called maturità, is carried out at national level and the text of the exercises are the same all over the country. 9 Bazzini, L., Pesci, A. and Reggiani, M. (editors): 1985, Guida al volume: G. Prodi, E. Magenes Elementi di analisi matematica, D'Anna, Firenze-Messina.

Prodi, G., Matematica come scoperta, D'Anna, Firenze-Messina, vol. 1, 1975, vol. 2, 1977.

U. M. I (ed.): 1977, Guida al progetto d'insegnamento della matematica proposto da G. Prodi, vol. 1, D'Anna, Firenze-Messina.

[10] Tall, D. O. (ed.): 1991, Advanced mathematical thinking, Kluwer, Dordrecht-Boston-London.

[11] NRD are teams of teachers and researchers; for details on NRD see the first report in this volume.

[12] Piochi, B.: 1994, Funzioni, limiti, derivate: come, perché, quando, con quali strumenti insegnare l'analisi nei diversi ordini di scuola, Quaderni IRRSAE Toscana.

[13] Artigue, M. and Ervynck, G.: 1992, Proceedings of Working Group 3 on students difficulties in calculus, ICME 7, Québec.

[14] Tall, D. and Vinner, S: 1981, `Concept image and concept definition with particular reference to limits and continuity", Educational Studies in Mathematics, 12, 151-169.

[15] Vergnaud, G.: 1990, `La théorie des champs conceptuels, Recherches en didactique des mathématiques, 10, 133-170.

[16] Bachelard, G.: 1980, La formation de l'esprit scientifique, J. Vrien, Paris (first published in 1938).

[17] Demana, F. and Waits, B. K.: 1992, `The role of technology in teaching mathematics', Mathematics Teacher, 81, 332-334.

[18] Borga, M. and Furinghetti, F. (eds.): 1986, ll problema dei fondamenti della matematica, Ecig, Genova.

[19] Grabiner, J.: 1974, `Is mathematical truth time-dependent?', The American mathematical monthly, 81, 354-365.