Визуелизација неких ирационалних бројева
Abstract
Намјера нам је да наставницима и њиховим ученицима покажемо да су то објекти који постоје, па се зато и зову реалнибројеви, тј. бројеви који постоје, јер је скоро без потешкоћа могуће конструисати геометријске илустрације неких ирационалних бројева.
References
[1] M. Anđić. O iracionalnim brojevima. Mat-Kol (Banja Luka), 23(2)(2916), 91-105.
[2] A. Arcavi, M. Bruckheimer and R. Ben-Zvi. History of mathematics for teachers: the case of irrational numbers. For the learning of mathematics, 7(2)(1987), 18-23.
[3] B. Čekrlija. Vremeplov kroz matematiku. Banja Luka: Grafimark, 2000.
[4] M. Doritou and E. Gray. Teachers’ subject knowledge: the number line representation. In: V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.) Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, January 28th-February 1st 2009 Lyon, France (pp. 1734-
1743), Lyon: Institut National De Recherche Pedagogique, 2010.
[5] E. Fischbein, R. Jehiam & D. Cohen. The concept of irrational number in highschool students and prospective teachers. Educational Studies in Mathematics, 29(1995), 29-44.
[6] N. Hayfa. Dimensions of knowledge and ways of thinking of irrational numbers. Athens Journal of Education, 3(2)(2016), 137-154.
[7] H. P. Manning. Irrational numbers and their representation by sequences and series. New York: John Wiley and Sons, 1906.
[8] M. Pezer i J. Matejaš. Brojevi π, e, i kroz povijest.
Доступно на адреси: https://www.halapa.com/pravipdf/brojevi.pdf
[9] N. Sirotic & R. Zazkis. Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1) (2007), 49-76.
[10] N. Sirotic & R. Zazkis. Irrational numbers on the number line – where are they? International Journal of Mathematical Education in Science and Technology, 38(4)(2007), 477-488.
[11] M. K. Srivastav. Representation of irrational numbers on number lines and study of mathematical error. International Journal of Engineering Research and Allied Sciences (IJERAS), 2(3)(2017), 5-6.
[12] M Gr. Voskoglou and G. D. Kosyvas. Analyzing students' difficulties in understanding real numbers. REDIMAT- Journal of Research in Mathematics Education, 1(3)(2012), 301 -336.
[13] R. Zazkis. Representing numbers: prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2–3)(2005), 207–218.
[14] R. Zazkis & N. Sirotić. Representing and defining irrational numbers: exposing the missing link. CBMS Issues in Mathematics Education, 16(2010).
[15] R. Zazkis and N. Sirotić. Making sense of irrational numbers: Focusing on representation. In: M. J. Høines and A. B. Fuglestad (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp 497–504), Bergen: Bergen University College 2005.
[2] A. Arcavi, M. Bruckheimer and R. Ben-Zvi. History of mathematics for teachers: the case of irrational numbers. For the learning of mathematics, 7(2)(1987), 18-23.
[3] B. Čekrlija. Vremeplov kroz matematiku. Banja Luka: Grafimark, 2000.
[4] M. Doritou and E. Gray. Teachers’ subject knowledge: the number line representation. In: V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.) Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, January 28th-February 1st 2009 Lyon, France (pp. 1734-
1743), Lyon: Institut National De Recherche Pedagogique, 2010.
[5] E. Fischbein, R. Jehiam & D. Cohen. The concept of irrational number in highschool students and prospective teachers. Educational Studies in Mathematics, 29(1995), 29-44.
[6] N. Hayfa. Dimensions of knowledge and ways of thinking of irrational numbers. Athens Journal of Education, 3(2)(2016), 137-154.
[7] H. P. Manning. Irrational numbers and their representation by sequences and series. New York: John Wiley and Sons, 1906.
[8] M. Pezer i J. Matejaš. Brojevi π, e, i kroz povijest.
Доступно на адреси: https://www.halapa.com/pravipdf/brojevi.pdf
[9] N. Sirotic & R. Zazkis. Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1) (2007), 49-76.
[10] N. Sirotic & R. Zazkis. Irrational numbers on the number line – where are they? International Journal of Mathematical Education in Science and Technology, 38(4)(2007), 477-488.
[11] M. K. Srivastav. Representation of irrational numbers on number lines and study of mathematical error. International Journal of Engineering Research and Allied Sciences (IJERAS), 2(3)(2017), 5-6.
[12] M Gr. Voskoglou and G. D. Kosyvas. Analyzing students' difficulties in understanding real numbers. REDIMAT- Journal of Research in Mathematics Education, 1(3)(2012), 301 -336.
[13] R. Zazkis. Representing numbers: prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2–3)(2005), 207–218.
[14] R. Zazkis & N. Sirotić. Representing and defining irrational numbers: exposing the missing link. CBMS Issues in Mathematics Education, 16(2010).
[15] R. Zazkis and N. Sirotić. Making sense of irrational numbers: Focusing on representation. In: M. J. Høines and A. B. Fuglestad (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp 497–504), Bergen: Bergen University College 2005.