Iconic and Symbolic Representation in Early Mathematics Teaching
Abstract
Mathematics is an abstract science, it uses a specific symbolic language, a kind of code that is difficult for children to comprehend. Using operation signs and numbers is not simple and obvious for them. The learning of mathematics by children cannot therefore be based on symbols alone. Action is needed first. However, since there is a large gap between an action and a symbol, it is necessary to support the teaching of mathematics with graphic means. Introducing a graphic element as a kind of methodological aid requires careful preparation, motivation and embedding it in previous physical activities performed by children. Otherwise, such an item, instead of facilitating the understanding of a concept, hinders that understanding and becomes an illusory aid. This paper describes the role and importance of pictorial representation in early mathematics teaching. Based on selected examples of tasks from textbooks, the difficulties of illustrating mathematical concepts are presented, and appropriate methodological solutions in this area are indicated.
References
Bruner J.S. (1978). Poza dostarczone informacje. Studia z psychologii poznawania, trans. B. Mroziak, Warszawa: Państwowe Wydawnictwo Naukowe.
Bugajska-Jaszczołt B., Czajkowska M. (2013). Komunikacja na zajęciach z edukacji matematycznej, “Problemy Wczesnej Edukacji”, vol. 4, no. 4(23), pp. 39–50.
Dąbrowski M. (2008). Pozwólmy dzieciom myśleć. O umiejętnościach matematycznych polskich trzecioklasistów, Warszawa: Centralna Komisja Egzaminacyjna.
Dobrowolska M., Jucewicz M., Szulc A. (2014). Lokomotywa. Klasa III. Z. 1, Gdańsk: Gdańskie Wydawnictwo Oświatowe.
Donaldson M. (1986). Myślenie dzieci, trans. A. Hunca-Bednarska, E.M. Hunca, Warszawa: Wiedza Powszechna.
Gruszczyk-Kolczyńska E. (1994). Dzieci ze specyficznymi trudnościami w uczeniu się matematyki, Warszawa: Wydawnictwa Szkolne i Pedagogiczne.
Hejny M. (1997). Rozwój wiedzy matematycznej, “Dydaktyka Matematyki”, no. 19, pp. 15–28.
Krygowska Z. (1986). Elementy aktywności matematycznej, które powinny odgrywać znaczącą rolę w matematyce dla wszystkich, “Dydaktyka Matematyki”, no. 6, pp. 25–41.
Lankiewicz B., Semadeni Z. (1994). Matematyka 2. Klasa 2, Warszawa: Wydawnictwa Szkolne i Pedagogiczne.
Nawolska B., Żądło J. (2010). Błąd w edukacji matematycznej, [in:] K. Gąsiorek, Z. Nowak (eds.), Tworzenie obrazu świata u dzieci w młodszym wieku szkolnym. Szanse i bariery, Kraków: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, pp. 78–94.
Nawolska B., Żądło-Treder J. (2017). Dziecięca koncepcja matematyki tworzona przez zadania z podręczników szkolonych, [in:] I. Czaja-Chudyba, B. Pawlak, J. Vaškevič-Buś (eds.), Wizja świata – wizja dziecka w przestrzeni podręczników do edukacji wczesnoszkolnej, Kraków: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, pp. 108–120.
Pisarski M. (1996). Ułatwienia metodyczne w nauczaniu początkowym matematyki, “Problemy Studiów Nauczycielskich. Dydaktyka Matematyki”, no. 6, pp. 144–158.
Semadeni Z. (1992). Grafy strzałkowe i drzewa jako reprezentacje ikoniczno-enaktywne, “Dydaktyka Matematyki”, no. 14, pp. 114–119.
Semadeni Z. (2001). Słoneczna matematyka. Klasa 1. Zeszyt jesienny, Warszawa: Muza Szkolna.
Swoboda E. (2017). Tworzenie różnych reprezentacji przez dzieci podczas rozwiązywania problemu matematycznego, “Edukacja”, no. 1(140), pp. 27–38. DOI: 10.24131/3724.170102.
Turnau S. (1990). Wykłady o nauczaniu matematyki, Warszawa: Państwowe Wydawnictwo Naukowe.
Rodríguez-Hernández M.M., Pruneda R.E., Rodríguez-Díaz J.M. (2021). Statistical analysis of the evolutive effects of language development in the resolution of mathematical problems in primary school education, “Mathematics”, 2021, vol. 9, no. 1081, pp. 1–14, https://doi.org/10.3390/math9101081 (accessed: 5.07.2021).
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