Zdroje epistemologických překážek v porozumění nekonečnu

Magdalena Krátká

doi:10.14712/18047106.7

Vol. 1 No. 1 (2010): sciED Research Reports

Sources of Epistemological Obstacles in Understanding Infinity

Magdalena Krátká,

DOI: https://doi.org/10.14712/18047106.7

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Krátká, M. (2013). Sources of Epistemological Obstacles in Understanding Infinity. Scientia in Educatione, 1(1), 87-100. https://doi.org/10.14712/18047106.7

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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. Search in Google Scholar
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). Search in Google Scholar
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. Search in Google Scholar
CIHLÁŘ, J.; EISENMANN, P.; KRÁTKÁ, M. The Process of the Infinity Concept Formation by means of Obstacles and Their Overcoming. [v tisku]. Search in Google Scholar
EUKLEIDES. Základy. Knihy I–IV. [Komentované P. Vopěnkou. Překlad F. Servít, 1907.] Nymburk : OPS, 2007. Search in Google Scholar
FISCHBEIN, E.; TIROSH, D.; HESS, P. The Intuition of Infinity. Educational Studies in Mathematics, 1979, Vol. 10, p. 3–40. Search in Google Scholar
JELEMENSKÁ, P.; SANDER, E.; KATTMANN, U. Model didaktické rekonštrukcie: Impulz pre výzkum v oborových didaktikách. Pedagogika, 2003, roč. 53. č. 2, s. 190–201. Search in Google Scholar
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. Search in Google Scholar
KAPADIA, R.; BOROVCNIK, M. Chance Encounters: Probability in Education. Dordrecht : Kluwer Academic Publishers, 1991. Search in Google Scholar
KRÁTKÁ, M. Srovnání ontogenetického a fylogenetického vývoje porozumění jevu nekonečno v geometrickém kontextu. Praha, 2009, 150 s. Disertační práce (Ph.D.). Search in Google Scholar
Univerzita Karlova v Praze. Pedagogická fakulta. Katedra matematiky a didaktiky matematiky. Vedoucí disertační práce P. Vopěnka. Search in Google Scholar
MARX, A. Schülervorstellungen zu „unendlichen Prozessen. Berlin : Verlag Franzbecker, 2006. Search in Google Scholar
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. Search in Google Scholar
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. Search in Google Scholar
SIERPINSKA, A. Understanding in Mathematics. Washington, D.C. : The Falmer Press London, 1994. Search in Google Scholar
SPAGNOLO, F.; ČIŽMÁR, J. Komunikacia v matematike na strednej škole. Brno : Masarykova univerzita, 2003. Search in Google Scholar
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. Search in Google Scholar
VOPĚNKA, P. Pojednání o jevech povstávajících na množství. Plzeň a Nymburk : OPS, 2008. Search in Google Scholar
VOPĚNKA, P. Úhelný kámen evropské vzdělanosti a moci. Praha : Práh, 2000. Search in Google Scholar

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[1] BROUSSEAU, G. Theory of Didactical Situations in Mathematics. Didactique des mathématiques, 1970–1990. [Balacheff, N. et al.(ed.)] Dordrecht : Kluwer Academic Publisher, 1997. Search in Google Scholar

[2] 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). Search in Google Scholar

[3] 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. Search in Google Scholar

[4] CIHLÁŘ, J.; EISENMANN, P.; KRÁTKÁ, M. The Process of the Infinity Concept Formation by means of Obstacles and Their Overcoming. [v tisku]. Search in Google Scholar

[5] EUKLEIDES. Základy. Knihy I–IV. [Komentované P. Vopěnkou. Překlad F. Servít, 1907.] Nymburk : OPS, 2007. Search in Google Scholar

[6] FISCHBEIN, E.; TIROSH, D.; HESS, P. The Intuition of Infinity. Educational Studies in Mathematics, 1979, Vol. 10, p. 3–40. Search in Google Scholar

[7] JELEMENSKÁ, P.; SANDER, E.; KATTMANN, U. Model didaktické rekonštrukcie: Impulz pre výzkum v oborových didaktikách. Pedagogika, 2003, roč. 53. č. 2, s. 190–201. Search in Google Scholar

[8] 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. Search in Google Scholar

[9] KAPADIA, R.; BOROVCNIK, M. Chance Encounters: Probability in Education. Dordrecht : Kluwer Academic Publishers, 1991. Search in Google Scholar

[10] KRÁTKÁ, M. Srovnání ontogenetického a fylogenetického vývoje porozumění jevu nekonečno v geometrickém kontextu. Praha, 2009, 150 s. Disertační práce (Ph.D.). Search in Google Scholar

[11] Univerzita Karlova v Praze. Pedagogická fakulta. Katedra matematiky a didaktiky matematiky. Vedoucí disertační práce P. Vopěnka. Search in Google Scholar

[12] MARX, A. Schülervorstellungen zu „unendlichen Prozessen. Berlin : Verlag Franzbecker, 2006. Search in Google Scholar

[13] 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. Search in Google Scholar

[14] 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. Search in Google Scholar

[15] SIERPINSKA, A. Understanding in Mathematics. Washington, D.C. : The Falmer Press London, 1994. Search in Google Scholar

[16] SPAGNOLO, F.; ČIŽMÁR, J. Komunikacia v matematike na strednej škole. Brno : Masarykova univerzita, 2003. Search in Google Scholar

[17] 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. Search in Google Scholar

[18] VOPĚNKA, P. Pojednání o jevech povstávajících na množství. Plzeň a Nymburk : OPS, 2008. Search in Google Scholar

[19] VOPĚNKA, P. Úhelný kámen evropské vzdělanosti a moci. Praha : Práh, 2000. Search in Google Scholar

Scientia in educatione

Sources of Epistemological Obstacles in Understanding Infinity

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