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2019, vol. 32, br. 1, str. 64-74
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Algoritamski i konceptualni pristup merenju površine figura
Аlgorithmic and conceptual approach to figure surface measurement
Projekat: Koncepcije i strategije obezbeđivanja kvaliteta bazičnog obrazovanja i vaspitanja (MPNTR - 179020)
Ključne reči: merenje; površina figure; algoritamski i konceptualni pristup
Sažetak
Merenje površine predstavlja važnu temu školskih programa i tesno je povezana sa drugim matematičkim temama i sa realnim okruženjem. Rezultati brojnih međunarodnih studija pokazuju da su postignuća učenika u domenu merenja površine niska, što se povezuje sa algoritamskim pristupom navedenoj temi, a koji karakteriše dominantno naglašavanje proceduralnih veština i primena formula. U radu su razmatrani različiti nivoi i parametri konceptualnog razumevanja merenja površine. Cilj istraživanja jeste ispitivanje nivoa i karaktera znanja o merenju površine kod učenika četvrtog razreda osnovne škole. U istraživanju su korišćene deskriptivna metoda i tehnika testiranja. Test čine standardizovani zadaci (Huang & Witz, 2013) i još dva zadatka koja nisu deo standardizovanog testa i koja su osmišljena na osnovu transkripta intervjua iz navedenog istraživanja. Uzorak je prigodan i čine ga dva odeljenja četvrtog razreda jedne osnovne škole u Beogradu. Osnovni zaključak jeste da su učenici razvili instrumentalno razumevanje postupka merenja površine i da strategije određivanja površine figura svode na primenu formula, zbog čega često greše, birajući pogrešnu formulu. Kao implikaciju istraživanja vidimo isticanje potrebe da se dovoljno vremena posveti aktivnostima konceptualnog pristupa podeli figura i popločavanju koje će premostiti veliki jaz od popločavanja površi i brojanja jedinica mere do razumevanja formula za računanje.
Abstract
Surface measurement is an important topic of the school curricula which is closely related to other mathematical topics and to the real world. The results of numerous international studies show that students' achievements in the area of surface measurement are low, which is explained by the algorithmic approach to the topic characterised by the emphasis on procedural skills and the application of formulas. The paper looks at different levels and parameters of the conceptual understanding of surface measurement.. The aim of the research is to examine the level and quality of knowledge about surface measurements among pupils of the fourth grade of primary school. The descriptive method and testing technique were used in the research. The test consists of standardised tasks (Huang & Witz, 2013) and two more tasks that are not part of the standardised test and that were designed based on the transcript of the interviews from the above study. The convenience sample consisted of two classes of the fourth-grade pupils of a primary school in Belgrade. The key conclusion is that students have developed an instrumental understanding of the surface measurement procedure and that the strategies for determining the surface of the figures reduce the application of the formula, which is why they choose, often mistakenly, the wrong formula. Based on the research findings, we conclude that more time should be devoted to activities involving the conceptual approach to the division of figures and tiling. These activities will bridge the great gap between surface tiling and counting the units of measure and the understanding of calculation formulas.
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