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Abstrakty
In the paper we present the main idea of the concept which we have called confrontational concept of mathematical epistemology. We refer it to philosophy of mathematics (in the context of epistemology of research) as well as to didactic problems (in the context of teacher preparation). Although we tried not to involve our discussion directly with any existing concepts of the philosophy of mathematics, however, in the paper one can notice some elements of modern formalism as well as Lakatos quasi-empiricism or a modern approach to structuralism.
Rocznik
Tom
Strony
11--24
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- University of Łódz, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Łódź
autor
- University of Łódz, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Łódź
Bibliografia
- [1] E. T. Bell, Mathematics, Queen and servant of science, McGraw-Hill, New York, 1951.
- [2] A. Blass, Ultrafilters: where topological dynamics = algebra = combinatorics, Topology Proc. 18 (1993), 33-56.
- [3] K. Ciesielski, K. Pogoda, Królowa bez Nobla. Rozmowy o matematyce, Warszawa, 2013.
- [4] M. Čiklová, Dynamical systems generated by functions with connected Gδ-graphs, Real Anal. Exch. 30(2) (2004/2005), 617-638.
- [5] Á. Császár, Generalized open sets, Acta Math. Hungar. 75 (1997), 65-87.
- [6] R. Duda, Zasada paralelizmu w dydaktyce, Dyd. Mat. 1 (1982), 127-138.
- [7] S. Friedland, Entropy of graphs, semigroups and groups, in: Ergodic theory of Zd Actions, M. Policott and K. Schmidt (eds.), London Math. Soc. Lecture Note Ser. 228, Cambridge Univ. Press (1996), 319-343.
- [8] E. Ghys, R. Langevin, P.Walczak, Entropie geometrique des feuilletages, Acta Math. 160 (1988), 105-142.
- [9] E. Jagoda, M. Pytlak, E. Swoboda, S. Turnau, A. Urbańska, Trójkąt epistemologiczny w badaniu tworzenia się wiedzy, Dyd. Mat. 27 (2004), 93-126.
- [10] E. Korczak-Kubiak, A. Loranty, R. J. Pawlak, On the topological entropy of discontinuous functions. Strong entropy points and Zahorski classes, to appear.
- [11] R. Murawski, Filozofia matematyki. Antologia tekstów klasycznych, Poznań, 1994.
- [12] R. Murawski, Filozofia matematyki. Zarys dziejów, Warszawa, 2001.
- [13] R. Murawski, Współczesna filozofia matematyki. Wybór tekstów. PWN, 2002.
- [14] T. Natkaniec, Almost continuity, Real Anal. Exch., 17 (1991/92), 462-520.
- [15] R. J. Pawlak, A. Loranty, The generalized entropy in the generalized topological spaces, Topology and its Applications 159 (2012), 1734-1742.
- [16] M. Resnik, Mathematics as a science of patterns: epistemology, Nous 16 (1982), 95-105.
- [17] A. Sierpińska, Pojęcie przeszkody epistemologicznej w nauczaniu matematyki, Dyd. Mat. 8 (1988), 103-153.
- [18] H. Steinbring, Dialogue between theory and practice in mathematical education in didactics of mathematics as a scientific discipline, edited by R. Biehler, R. W. Scolz, R. Strässer, B. Winkelmann, Kluwer Academic Publishers, Math. Education Library, 1994.
- [19] P. Szuca, Sharkovskii’s theorem holds for discontinuous functions, Fund. Math. 179 (2003), 27-41.
- [20] A. Violant, Zagadka Fermata. Trzy wieki zmagań matematyków, RBA of a series of Świat jest matematyczny, 2012.
- [21] H. Weyl, Mathematics and logic, Maer. Math. Month. 53 (1946), 1-13.
- [22] H. Weyl, Philosophy of mathematics and natural science, Princeton Univ. Press, New Jersey, 1949.
- [23] E. Wittmann, Developing mathematics education in a systemic process, Educat. Stud. in Math. 48 2001, 2-20.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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