Kontekst Przekazu w Matematyce

Jerzy Pogonowski


We introduce the concept of the context of transmission. It coversthe ways in which mathematical knowledge and mathematical abilities aretransmitted in education and popularization of mathematics. We stress therole of intuitive explanations in these processes. Several examples of suchexplanations are presented, related to: linguistic explanations, perception,empirical models, and internal explanations inside mathematics itself.


kontekst przekazu, objasnienie intuicyjne, dydaktyka matematyki


Ajdukiewicz, K.: 1975, Logika pragmatyczna, PWN, Warszawa.

Ben-Zeev, T., Star, J.: 2001, Intuitive Mathematics: Theoretical and Educational Implications, in: B. Torff, R. J. Sternberg (ed.), Understanding and Teaching the Intuitive Mind: Student and Teacher Learning, Lawrence Erlbaum Associates Publishers, Mahwah, New Jersey, London, 29–56.

Davis, P. J., Hersh, R.: 1994, Swiat Matematyki, PWN, Warszawa.

Fischbein, E.: 1987, Intuition in Science and Mathematics: an educational approach, Kluwer Academic Publishers, New York / Boston / Dordrecht / London / Moscow.

Fraenkel, A. A., Bar-Hillel, Y., Levy, A.: 1973, Foundations of set theory, North-Holland Publishing Company, Amsterdam, London.

Galperin, G.: 2003, Playing Pool with (The Number from a Billiard Point of View), Regular and Chaotic Dynamics 8(4), 375–394.

Ghrist, R.: 2014, Elementary Applied Topology, Createspace.

Good, I. J., Churchhouse, R. F.: 1968, The Riemann hypothesis and pseudorandom features of the Möbius sequence, Mathematics of Computation 22, 857–861.

Havil, J.: 2007, Nonplussed! Mathematical Proof of Implausible Ideas, Princeton University Press, Princeton and Oxford.

Havil, J.: 2008, Impossible? Surprising Solutions to Counterintuitive Conundrums, Princeton University Press, Princeton and Oxford.

Heath, T. L.: 2002, The Works of Archimedes, Dover Publications, Inc., Mineola, New York.

Klymchuk, M., Staples, S.: 2013, Paradoxes and Sophisms in Calculus, Mathematical Association of America, Washington, DC.

Lakoff, G., Johnson, M.: 1980, Metaphors we live by, University of Chicago Press, Chicago.

Lakoff, G., Núñez, R.: 2000, Where Mathematics Comes From. How the Embodied Mind Brings Mathematics into Being, Basic Books, New York.

Lange, M.: 2014, Depth and Explanation in Mathematics, Philosophia Mathematica 23(2), 196–214.

Laraudogoitia, J. P.: 1996, A Beautiful Supertask, Mind 105, 81–83.

Lénárt, I.: 1996, Non - Euclidean Adventures on the Lénárt Sphere, Key Curriculum Press, USA.

Levi, M.: 2009, The Mathematical Mechanic. Using Physical Reasoning to Solve Problems, Princeton University Press, Princeton and Oxford.

Mancosu, P.: 2015, Explanation in mathematics, in: E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Summer 2015 edn, Metaphysics Research Lab, Stanford

University. https://plato.stanford.edu/archives/sum2015/entries/mathematics-explanation/.

Needham, T.: 1997, Visual complex analysis, Clarendon Press, Oxford.

Pogonowski, J.: 2011, Geneza matematyki wedle kognitywistów, Investigationes Linguisticae XXXIII, 106–147.

Pogonowski, J.: 2012, Matematyczne metafory kognitywistów, Tekst odczytu wygłoszonego podczas LVIII Konferencji Historii Logiki, Uniwersytet Jagiellonski, Kraków, 23–24 pazdziernika 2012. http://www.logic.amu.edu.pl/images/0/0e/Mmk2012.pdf.

Pogonowski, J.: 2013, Matematyczne fantazje kognitywistów, w: J. Juchnowski, R. Wiszniowski (red.), Współczesna teoria i praktyka badan społecznych i humanistycznych,

Vol. 2, Wydawnictwo Adam Marszałek, Torun, 117–127.

Polya, G.: 2009, Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Ishi Press International, New York, Tokyo.

Polya, G.: 2014, Mathematics and Plausible Reasoning. Vol. I: Induction and Analogy in Mathematics, Vol. II: Patterns of Plausible Inference, Martino Publishing, Mansfield Centre, CT.

Romero, G. E.: 2014, The collapse of supertasks, Foundation of science 19(2), 209–216.

Schoenfeld, A. H.: 1985, Mathematical Problem Solving, Academic Press Inc., Orlando.

Sierpinska, A.: 1994, Understanding in Mathematics, The Falmer Press, London.

Steiner, M.: 1978, Mathematical Explanation, Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 34(2), 135–151.

Tall, D.: 2013, How Humans Learn to Think Mathematically. Exploring the Three Worlds of Mathematics, Cambridge University Press, Cambridge.

Full Text: PDF (Polski)

e-ISSN: 2450-341X, ISSN: 2080-9751

AUPC SDMP is on the List of the Ministry’s scored journals (part B) with 5 points for 2016