Una experiencia didáctica sobre funciones, en la escuela secundaria

Referencias

Apostol, T.M. (1977). Calcolo: I, Boringhieri, Torino (Calculus, 2nd edition, John Wiley & Sons, New York 1969). Arcavi, A.; Tirosh, D. & Nachmias, R.(1989). The effects of exploring a new representation on prospective teachers’ conception of functions: Vinner, S. (Ed.) Science and mathematics teaching: Interaction between research and practice, Hebrew University, Jerusalem. Bagni, G.T. (1995). Sul compito di matematica dell’esame di maturità scientifica 1995: La matematica e la sua didattica 4, 520-521. Bagni, G.T. (1997). Dominio di una funzione, numeri reali e numeri complessi. Esercizi standard and contratto didattico nella scuola secondaria superiore: La matematica e la sua didattica 3, 306-319. Bagni, G.T. (1998) Visualization and didactics of mathematics in High School: an experimental research: Scientia Paedagogica Experimentalis 35, 1, 161-180. Bagni, G.T. (2000). «Simple» rules and general rules in some High School students’ mistakes: Journal fur Mathematik Didaktik 21, 2, 124-138. Bergeron, J.C. & Herscovics, N. (1982). Levels in the understanding of the function concept: Workshop on functions by the Foundation for curriculum development, Enschede. Bottazzini, U.; Freguglia, P. & Toti Rigatelli, L. (1992). Fonti per la storia della matematica: Sansoni, Firenze. Bourbaki, N. (1963). Elementi di storia della matematica: Feltrinelli, Milano (Eléments d’histoire des mathematiques, Hermann, Paris 1960). Bourbaki, N. (1966). Eléments de mathématiques, Théorie des Ensembles, II, Hermann, Paris. Castelnuovo, G. (1938). Le origini del calcolo infinitesimale: Zanichelli, Bologna (reprint: Feltrinelli, Milano 1962). D’Amore, B. (1999). Elementi di didattica della matematica: Pitagora, Bologna. Davis, R.B. (1982). Teaching the concept of function: method and reasons: Workshop on functions by the Foundation for curriculum development, Enschede. Dini, U. (1878). Fondamenti per la teorica delle funzioni di variabile reale: Nistri, Pisa (reprint: UMI, Firenze 1990). Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking, Tall, D. (Ed.), Advanced Mathematical Thinking, Kluwer Academic Publishers, 95-126. Duval, R. (1993). Registres de répresentation sémiotique et fonctionnement cognitif de la pensée: Annales de Didactique et de Sciences Cognitives 5, IREM, Strasbourg. Duval, R. (1995a). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels, Peter Lang, Paris. Duval, R. (1995b). Quel cognitif retenir en didactique des mathématiques?: Actes de l’École d’ètè (La matematica e la sua didattica 3, 1996, 250-269). Euler, L. (1796). Introduction a l’Analyse infinitésimale: Barrois, Paris (1st French edition). Fischbein, E. (1993). The theory of figural concepts: Educational Studies in Mathematics 24, 139-162. Frege, G. (1973). Senso e denotazione: Bonomi, A. (Ed.), La struttura logica del linguaggio, Bompiani, Milano 9-32. Furinghetti, F. & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: from philogenesis and ontogenesis theory to classroom practice. English, L. (Ed.), Handbook of International Research in Mathematics Education, 631-654, Lawrence Erlbaum, New Jersey. Gelbaum, B.R. (1961). Advanced calculus: Appleton-Century-Crofts, New York. Gelbaum, B.R. (1962). The real number system: Appleton-Century Crofts, New York. Giusti, E.: 1983, Analisi Matematica 1: Boringhieri, Torino. Gray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: A perceptual view of simple arithmetics, Journal for Research in Mathematics Education, 27 (2), 116-140. Grugnetti, L. & Rogers, L. (2000). Philosophical, multicultural and interdisciplinary issues. In Fauvel, J. & van Maanen, J. (Eds.), History in Mathematics Education. The ICMI Study, 39-62, Dodrecht, Kluver. Hairer, E. & Wanner, G. (1996). Analysis by its History: Springer-Verlag, New York. Harel, G. & Dubinsky, E. (Eds.). (1992). The concept of Function: aspects of Epistemology and Pedagogy: MAA Notes 25. Harel, G. & Kaput, J. (1991). The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts: Tall, D. (Ed.), Advanced Mathematical Thinking, Kluwer Academic Publishers, Dodrecht, 82-94. Kaput, J. (1989a). Linking Representations in the Symbol Systems of Algebra: Kieran, C. & Wagner, S. (Eds.), Research Agenda for Mathematics Education: Research Issues in the Learning and Teaching of Algebra, Lawrence Erlbaum Publishers, Hillsdale, 167- 194. Kaput, J. (1989b). Linking representations in the symbol systems of algebra: Wagner, S. & Kieran, C. (Eds.), Research issues in the learning and teaching of algebra, National Council of Teachers of Mathematics, Reston, 167-181. Kline, M. (1972). Mathematical thought from ancient to modern times: Oxford University Press, New York. Lakoff, G. & Nuñez, R. (2000). Where Mathematics come from? How the Embodied Mind Brings Mathematics into Being, Basic Books, New York. Malara, N.A. (1997). Problemi di insegnamento-apprendimento nel passaggio dall’aritmetica all’algebra: La matematica e la sua didattica, 2, 176-186. Markovitz, Z.; Eylon, B. & Bruckheimer, N. (1986). Functions today and yesterday: For the learning of mathematics 6 (2), 18-24. Norman, A. (1992). Teachers’ Mathematical Knowledge of the Concept of Function: Dubinsky, E. & Harel, G. (Eds.), The concept of Function: aspects of Epistemology and Pedagogy, MAA Notes 25, 215-232. Radford, L. (1997). On Psychology, Historical Epistemology and the Teaching of Mathematics: Towards a Socio-Cultural History of Mathematics, For the Learning of Mathematics, 17(1), 26-33. Schwingendorf, K.; Hawks, J. & Beineke, J. (1992). Horizontal and Vertical Growth of the Student’s Conception of Function: Dubinsky, E. & Harel, G. (Eds.), The concept of Function: aspects of Epistemology and Pedagogy, MAA Notes 25, 133-149. Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coins: Educational Studies in Mathematics 22, 1-36. Slavit, D. (1997). An alternate route to reification of function, Educational Studies in Mathematics 33, 259-281. Smith, D.E. (1959). A source book in Mathematics: Dover, New York (McGraw-Hill, 1929). Stavy, R. & Tirosh, D. (1996). Intuitive rules in science and mathematics: the case of ‘More of A More of B’: International Journal for Science Education. 18.6, 553-667. Tall, D. (1990). Inconsistencies in the learning of Calculus and Analysis: Focus on Learning Problems in Mathematics 12, 49-64. Tirosh, D. (1990). Inconsistencies in students’ mathematical constructs: Focus on Learning Problems in Mathematics 12, 111-129. Tirosh, D. (Ed.). (1994). Implicit and explicit knowledge: an educational approach: Ablex Publishing Corp., Norwood. Vinner, S. (1983). Concept definition, concept image and the notion of function: International Journal for Mathematical Education in Science and Technology 14, 3, 293-305. Vinner, S. (1987). Continuous functions-images and reasoning in College students: Proceedings PME 11, II, Montreal, 177-183. Vinner, S. (1992). Function concept as prototype for problems in mathematics: Dubinsky, E. & Harel, G. (Eds.), The concept of Function: aspects of Epistemology and Pedagogy, MAA Notes 25, 195-213.