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A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence. In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969. |
Loci: ConvergenceTeaching the Fundamental Theorem of Calculus: A Historical ReflectionReferences[1] M. Artigue, “Analysis.” In D. Tall (Ed.), Advanced Mathematical Thinking, Kluwer Academic Publishers, Dordrecht, 1992. pp. 167-198. [2] M. E. Baron, The Origins of Infinitesimal Calculus, Dover Publications, New York, 1969. [3] N. Bourbaki, Elements of Mathematics, Functions of a Real Variable, Elementary Theory, Springer, Heidelberg, 2003. [4] R. E. Bradley and C. Sandifer, Cauchy’s Cours d’Analyse, An Annotated Translation, Springer Verlag, Doordrecht, 2009. [5] D. M. Bressoud, “Historical reflections on teaching the fundamental theorem of integral calculus,” American Mathematical Monthly 118 (2011), pp. 99–115. [6] F. Cajori, “The history of notations of the calculus,” Annals of Mathematics, Second Series 25 (1923), pp. 1–46. [7] F. Cajori, A History of Mathematics, The Macmillan Company, New York, 1931. [8] A. L. Cauchy, Résumé des Leçons Données a L’Ecole Royale Polytechnique, Oevres Complétes, vol. IV of 11, Gauthier-Villard, Paris, 1899. [9] J. M. T. Child, The Geometrical Lectures of Isaac Barrow, Translated with notes and proofs, and a discussion on the advance made therein on the work of his predecessors in the infinitesimal calculus., no. 3 in Series of Classics of Science and Philosophy, The Open Court Publishing Company, Chicago, 1916. [10] B. Cornu, “Limits.” In D. Tall (Ed.), The transition to advanced mathematical thinking: Functions, limits, infinity and proofs, Kluwer Academic Publishers, Dordrecht, 1992. pp. 153-166. [11] J. Cottrill, D. Nichols, K. Schwingendorf, K. Thomas, and D. Vidakovic, “Understanding the limit concept: Beginning with a coordinated process schema,” Journal of Mathematical Behavior 15 (1996), pp. 167–192. [12] R. B. Davis and S. Vinner, “The notion of limit: Some seemingly unavoidable misconception stages,” Journal of Mathematical Behavior (1986), pp. 281–303. [13] G. Ervynck, “Conceptual difficulties for first year university students in acquisition for the notion of limit of a function.” In L. P. Mendoza and E. R. Williams (Eds.), Canadian Mathematics Education Study Group: Proceedings of the Annual Meeting, Kingston, Ontario: Memorial University of Newfoundland, 1988. pp. 330-333. [14] L. Euler, Introductio in analysin infinitorum, vol. 1, Real Sociedad Matemática Española, Sevilla, edición facsimilar, “thales” ed., 1748. [15] L. Euler, Introductio in analysin infinitorum, Vol. 2; Introduction to the Analysis of the Infinite, Book II (translation of vol. 2), Springer Verlag, New York, 1748. [16] L. Euler, Institutiones calculi differentialis, 1755; Foundations of Differential Calculus (translation), Springer Verlag, New York, 2000. [17] H. Freudenthal, Mathematics as an Educational Task, D. Reidel Publishing Co., Doordrecht, 1973. [18] H. Freudenthal, Didactical Phenomenology of Mathematical Structures, D. Reidel Publishing Co., Doordrecht, 1999. [19] M. N. Fried, “Some reflections on Hernández and López’s reflections on the chain rule,” The Montana Mathematics Enthusiast 7 (2010), pp. 333–338. [20] L. Gillman, “An axiomatic approach to the integral,” American Mathematical Monthly 100 (1993), pp. 16–25. Available at http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=2913 [21] L. Gillman and R. H. MacDowell, Calculus, W. W. Norton, New York, 1973. [22] L. Gillman and R. H. MacDowell, Calculus, W. W. Norton, New York, second ed., 1978. [23] N. Guicciardini, Isaac Newton on Mathematical Certainty and Method, The MIT Press, Cambridge, Massachusetts, London, 2009. [24] H. Hahn and A. Rosenthal, Set Functions, The University of New Mexico Press, 1948. [25] O. Hernández Rodríguez and J. López Fernández, “A semiotic reflexion on the didactics of the chain rule,” The Montana Mathematics Enthusiast 7 (2010), pp. 321–332. [26] V. J. Katz, A History of Mathematics, An Introduction, Addison Wesley, Pearson, New York, third edition, 2009. [27] J. L. Lagrange, Theorie des fonctions analytiques, L’Imprimerie de la republique, Paris, 1797. [28] S. Lang, A First Course in Calculus, Addison Wesley, third printing (1974), 1968. [29] R. Laubenbacher and D. Pengelley, Mathematical Expeditions, Chronicles by the Explorers, Undergraduate Texts in Mathematics, Springer Verlag, 1999. [30] L. Le and D. Tall, “Constructing different concept images of sequences and limits by programming,” Proceedings of the Seventeenth Conference for the Psychology of Mathematics Education, Tsukuba, Japan (1993), pp. 41–48. [31] A. Leahy, “An Introduction to James Gregory’s Geometriae Pars Universalis,” Proceedings of the Eighth Midwest History of Mathematics Conference (2000). [32] A. Leahy, “A Euclidean Approach to the FTC,” Loci: Convergence (2004). DOI: 10.4169/loci002156 http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2156 [33] H. Levi, Polynomials, Power Series and Calculus, Van Nostrand Company, Inc., Princeton, 1968. [34] G. F. A. L’Hospital, Analyse des infiniment petits pour l’ intelligence des lignes courbes, L’Imprimerie Royale, Paris, 1696. [35] G. F. A. L’Hospital, The method of fluxions both direct and inverse (translated by Edmund Stone), printed for William Innys, London, 1730. [36] J. Mamona-Downs, “Pupils’ interpretations of limit concept: A comparison between Greeks and English,” Proceedings of the Fourteenth Conference for the Psychology of Mathematics Education, Mexico City, Mexico (1990), pp. 69–76. [37] J. J. O'Connor and E. F. Robertson, "Stanislaw Saks," MacTutor History of Mathematics Archive, 2000, http://www.gap-system.org/~history/Biographies/Saks.html [38] J. J. O'Connor and E. F. Robertson, "Hans Hahn," MacTutor History of Mathematics Archive, 2006, http://www.gap-system.org/~history/Biographies/Hahn.html [39] A. Robert, “L’acquisition de la notion de convergence des suites numeriques dans l’enseignement superieur,” Reserches en Didactique des Mathematiques 3 (1982), pp. 307–341. [40] A. Sierpinska, “Humanities students and epistemological obstacles related to limits,” Educational Studies in Mathematics (1987), pp. 371–397. [41] D. J. Struik, A Source Book in Mathematics, 1200-1800, Dover Publications Inc., New York, 1969. [42] D. O. Tall, “The transition to advanced mathematical thinking: Functions, limits, infinity and proof.” In D. A. Grows (Ed.), The Handbook of research on mathematics teaching and learning, Macmillan, New York, 1992, pp. 495-511. [43] D. O. Tall and S. Vinner, “Concept image and concept definition in mathematics, with particular reference to limits and continuity,” Educational Studies in Mathematics (1981), pp. 151–169. [44] D. T. Whiteside, “Patterns of mathematical thought in the latter seventeenth century,” Archive for History of Exact Sciences 1 (1961), pp. 179–388. [45] S. R. Williams, “Model of limit held by college calculus students,” Journal for Research in Mathematics Education (1991), pp. 219–236.
Pages: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Lopez Fernandez, Jorge M. and Omar A. Hernandez Rodriguez, "Teaching the Fundamental Theorem of Calculus: A Historical Reflection," Loci (January 2012), DOI: 10.4169/loci003803 |