Abstract
The article analyzes three areas of phenomena with which we meet in our effort to identify epistemological obstacles in understanding infinity — Conception of the Objects Existence and related creator’s principle, The Horizon and its Positions, and Knowledge of Finity. Each of the areas is described in detail. Further particular phenomena are illustrated by extracts of experimental interviews. Finally the discussion on these three areas and subsequences in finding specific epistemological obstacles follows.References
BROUSSEAU, G. Theory of Didactical Situations in Mathematics. Didactique des mathématiques, 1970–1990. [Balacheff, N. et al.(ed.)] Dordrecht : Kluwer Academic Publisher, 1997.
BROUSSEAU, G.; SARRAZY, B. Glossaire de quelques concepts de la théorie des situations didactiques en mathématiques. DAEST, Université Bordeaux 2, 2002. (English translation by V. Warfield).
CIHLÁŘ, J.; EISENMANN, P.; KRÁTKÁ, M.; VOPĚNKA, P. Cognitive conflict as a tool of overcoming obstacles in understanding infinity. Teaching Mathematics and Computer Science, 2009, Vol. 7, No. 2, p. 279–295.
CIHLÁŘ, J.; EISENMANN, P.; KRÁTKÁ, M. The Process of the Infinity Concept Formation by means of Obstacles and Their Overcoming. [v tisku].
EUKLEIDES. Základy. Knihy I–IV. [Komentované P. Vopěnkou. Překlad F. Servít, 1907.] Nymburk : OPS, 2007.
FISCHBEIN, E.; TIROSH, D.; HESS, P. The Intuition of Infinity. Educational Studies in Mathematics, 1979, Vol. 10, p. 3–40.
JELEMENSKÁ, P.; SANDER, E.; KATTMANN, U. Model didaktické rekonštrukcie: Impulz pre výzkum v oborových didaktikách. Pedagogika, 2003, roč. 53. č. 2, s. 190–201.
JIROTKOVÁ, D.; LITTLER, G. Student’s Concept of Intimity in the Context of a Simple Geometrical Construct. In Proceedings of the 2003 Joint Meeting of PME and PMENA, (Vol. 3, p. 125–132), Honolulu, Hawai, 2003.
KAPADIA, R.; BOROVCNIK, M. Chance Encounters: Probability in Education. Dordrecht : Kluwer Academic Publishers, 1991.
KRÁTKÁ, M. Srovnání ontogenetického a fylogenetického vývoje porozumění jevu nekonečno v geometrickém kontextu. Praha, 2009, 150 s. Disertační práce (Ph.D.).
Univerzita Karlova v Praze. Pedagogická fakulta. Katedra matematiky a didaktiky matematiky. Vedoucí disertační práce P. Vopěnka.
MARX, A. Schülervorstellungen zu „unendlichen Prozessen. Berlin : Verlag Franzbecker, 2006.
RADFORD, L. On Psychology, Historical Epistemology, and the Teaching of Mathematics: Towards a Socio-Cultural History of Mathematics. For the Learning of Mathematics 17, 1. Vancouver : FLM Publishing Association, 1997, p. 26–33.
RADFORD, L.; BOERO, P.; VASCO, C. Historical formation and student understanding of mathematics: Epistemological assumptions framing interpretations of students understanding of mathematics. In FAUVEL, J.; Van MAANEN, J. (ed.). History in Mathematics Education. Dordrecht, Boston, London : Kluwer, 2000.
SIERPINSKA, A. Understanding in Mathematics. Washington, D.C. : The Falmer Press London, 1994.
SPAGNOLO, F.; ČIŽMÁR, J. Komunikacia v matematike na strednej škole. Brno : Masarykova univerzita, 2003.
TRLIFAJOVÁ, K. Studie o nekonečnu v matematice. Praha : 2001. Disertační práce (Ph.D.). Univerzita Karlova v Praze. Matematicko-fyzikální fakulta. Katedra teoretické informatiky a matematické logiky.
VOPĚNKA, P. Pojednání o jevech povstávajících na množství. Plzeň a Nymburk : OPS, 2008.
VOPĚNKA, P. Úhelný kámen evropské vzdělanosti a moci. Praha : Práh, 2000.
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