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\u041f\u0440\u0435\u0443\u0437\u043c\u0438\u0442\u0435 \u043a\u043e\u043c\u043f\u043b\u0435\u0442\u0430\u043d \u0440\u0430\u0434\/Download<\/a><\/p>\n

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\u041c\u0438\u043b\u0430\u043d \u041f. \u041c\u0438\u043b\u0438\u043a\u0438\u045b, \u0421\u0430\u045a\u0430 \u041c. \u041c\u0430\u0440\u0438\u0447\u0438\u045b, \u041d\u0435\u043d\u0430\u0434 \u0420. \u0412\u0443\u043b\u043e\u0432\u0438\u045b<\/p>\n

DOI 10.5937\/ZRPFU2224127M <\/a><\/p>\n

\u0423\u0414\u041a 37.091.39:004.4<\/p>\n

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\u041f\u0440\u0438\u043c\u0435\u043d\u0430 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 GeoGebra \u043f\u0440\u0438 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u045a\u0443 \u043f\u043e\u0458\u043c\u0430 \u043e\u0431\u0438\u043c\u0430 \u0444\u0438\u0433\u0443\u0440\u0435 \u0443 \u043c\u043b\u0430\u0452\u0438\u043c \u0440\u0430\u0437\u0440\u0435\u0434\u0438\u043c\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435<\/h4>\n
\u0410\u043f\u0441\u0442\u0440\u0430\u043a\u0442: \u0411\u0440\u043e\u0458\u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u0438\u0441\u0442\u0440\u0430\u0436\u0438\u0432\u0430\u045a\u0430 \u043f\u043e\u00ad\u043a\u0430\u0437\u0430\u043b\u0430 \u0441\u0443 \u043f\u0440\u0435\u0434\u043d\u043e\u0441\u0442\u0438 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u0438\u0445 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0408\u0435\u0434\u0430\u043d \u043e\u0434 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043a\u0438\u0445 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u0438\u0445 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u043a\u043e\u0458\u0438 \u0458\u0435 \u0443 \u043f\u043e\u0441\u043b\u0435\u0434\u045a\u0435 \u0432\u0440\u0435\u043c\u0435 \u0441\u0442\u0435\u043a\u0430\u043e \u0432\u0435\u043b\u0438\u043a\u0443 \u043f\u043e\u043f\u0443\u043b\u0430\u0440\u043d\u043e\u0441\u0442 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0458\u0435 GeoGebra. \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0441\u043a\u0435 \u0442\u0440\u0430\u043d\u0441\u0444\u043e\u0440\u043c\u0430\u00ad\u0446\u0438\u0458\u0435 \u0438 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043a\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0458\u0435 \u043e\u0432\u043e\u0433 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0441\u043a\u043e\u0433 \u043f\u0430\u043a\u0435\u0442\u0430 \u043c\u043e\u0433\u0443 \u0441\u0435 \u0435\u0444\u0438\u00ad\u043a\u0430\u0441\u043d\u043e \u043f\u0440\u0438\u00ad\u043c\u0435\u043d\u0438\u0442\u0438 \u0443 \u0440\u0430\u0437\u043d\u0438\u043c \u043d\u0438\u0432\u043e\u0438\u043c\u0430 \u0448\u043a\u043e\u043b\u043e\u0432\u0430\u045a\u0430, \u043e\u0434 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435 \u0434\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0437\u0438\u0442\u0435\u0442\u00ad\u0441\u043a\u043e\u0433 \u043d\u0438\u0432\u043e\u0430. \u0426\u0438\u0459 \u043e\u0432\u043e\u0433 \u0440\u0430\u0434\u0430 \u0458\u0435 \u0434\u0430 \u043a\u0440\u043e\u0437 \u0438\u0437\u0430\u0431\u0440\u0430\u043d\u0435 \u043f\u0440\u0438\u00ad\u043c\u0435\u0440\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u00ad\u0432\u0438\u043c\u043e \u043d\u0435\u043a\u0435 \u043e\u0434 \u043c\u043e\u0433\u0443\u045b\u043d\u043e\u0441\u0442\u0438 GeoGebra \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0443 \u043c\u043b\u0430\u00ad\u0452\u0438\u043c \u0440\u0430\u0437\u0440\u0435\u0434\u0438\u043c\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435. \u041d\u0430 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0438\u043c\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u0458\u0435 \u043a\u0430\u043a\u043e \u0441\u0435 GeoGebra \u043c\u043e\u0436\u0435 \u043a\u043e\u0440\u0438\u0441\u0442\u0438\u0442\u0438 \u0443 \u0440\u0430\u0434\u0443 \u0441\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u043c\u0430 \u0443 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u045a\u0443 \u043f\u043e\u0458\u043c\u0430 \u043e\u0431\u0438\u043c \u0444\u0438\u0433\u0443\u0440\u0435 \u0443 \u0440\u0430\u0432\u043d\u0438 (\u043f\u0440\u0430\u0432\u043e\u0443\u0433\u0430\u043e\u043d\u0438\u043a, \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0438 \u0442\u0440\u043e\u0443\u0433\u0430\u043e).<\/p>\n
\u041a\u0459\u0443\u0447\u043d\u0435 \u0440\u0435\u0447\u0438: \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0430, GeoGebra, \u043e\u0431\u0438\u043c \u0444\u0438\u0433\u0443\u0440\u0435, \u043c\u043b\u0430\u0452\u0438 \u0440\u0430\u0437\u0440\u0435\u0434\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435.<\/p>\n
<\/p>\n

<\/span>The GeoGebra software application in the PERIMETER concept formation in lower grades of elementary school<\/h4>\n
Summary: Numerous experimental studies have shown the advantages of using educational software in teaching mathematics. One of the dynamic educational software that has recently gained great popularity in teaching mathematics is GeoGebra. The geometric transformations and dynamic functions of the software can be effectively applied at various education levels, from elementary school to university level. The aim of this paper is to present, through selected examples, some possibilities of GeoGebra software that can help students in lower grades of elementary school become proficient in the concept of the perimeter of a figure in a plane (rectangle, square and triangle), thus allowing them to follow each step in the pattern formation for calculating the perimeter.<\/p>\n
Keywords: mathematics, geometry, GeoGebra, perimeter, lower grades of elementary school.<\/p>\n
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\u0409\u0430\u0458\u043a\u043e, \u0415. (2014). \u0423\u0442\u0438\u0446\u0430\u0458 Geogebra-e \u043d\u0430 \u043f\u0440\u0435\u0434\u0430\u0432\u0430\u045a\u0435 \u0438 \u0443\u0447\u0435\u045a\u0435 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u043a\u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u0443 \u0441\u0440\u0435\u0434\u045a\u043e\u0458 \u0448\u043a\u043e\u043b\u0438. (\u041d\u0435\u043e\u0431\u0458\u0430\u0432\u0459\u0435\u043d\u0430 \u0434\u043e\u043a\u0442\u043e\u0440\u0441\u043a\u0430 \u0434\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0458\u0430). \u041d\u043e\u0432\u0438 \u0421\u0430\u0434: \u041f\u0440\u0438\u0440\u043e\u0434\u043d\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>\n
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Marti\u0301n-Caraballo, A. M. & Tenorio-Villalo\u0301n, A\u0301. F. (2015). Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities. Mathematics Education, 10(2), 53\u201365.<\/p>\n
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\u041c\u0430\u0440\u0438\u0447\u0438\u045b, \u0421. \u0438 \u0421\u0442\u043e\u0458\u043a\u0430\u043d\u043e\u0432\u0438\u045b, \u0408. (2021). \u0422\u0430\u0447\u043a\u0430\u0441\u0442\u0430 \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0430 \u043c\u0440\u0435\u0436\u0430 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u0443 \u043c\u043b\u0430\u0452\u0438\u043c \u0440\u0430\u0437\u0440\u0435\u0434\u0438\u043c\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435. \u0417\u0431\u043e\u0440\u043d\u0438\u043a \u0440\u0430\u0434\u043e\u0432\u0430, \u041f\u0435\u0434\u0430\u0433\u043e\u0448\u043a\u043e\u0433 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442\u0430 \u0443 \u0423\u0436\u0438\u0446\u0443, 23, 111\u2013126. DOI 10.5937\/ZRPFU2123111M.<\/p>\n
\u041c\u0438\u043b\u0438\u043a\u0438\u045b, \u041c., \u0412\u0443\u043b\u043e\u0432\u0438\u045b, \u041d. \u0438 \u041c\u0438\u0445\u0430\u0458\u043b\u043e\u0432\u0438\u045b, \u0410. (2020). \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0441\u043a\u0430 \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u0458\u0430 \u0440\u0430\u0437\u043b\u043e\u043c\u0430\u043a\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u043e\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u043e\u0433 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u0413\u0435\u043e\u0413\u0435\u0431\u0440\u0430. \u0423\u0437\u0434\u0430\u043d\u0438\u0446\u0430, 17(1), 307\u2013317.<\/p>\n
Moyer-Packenham, P. S., Ulmer, L. A. & Anderson, K. L. (2012). Examining Pictorial Models and Virtual Manipulatives for Third-Grade Fraction Instruction. Journal of Interactive Online Learning, 11(3),103\u2013120.<\/p>\n
Mukiri, \u041c. I. (2016). Feasibility of using geogebra in the teaching and learning of geometry concepts in secondary schools in Kajiado County, Kenya. (Doctoral thesis). School of \u0415ducation of \u041aenyatta University.<\/p>\n
\u041d\u0430\u0434\u0440\u0459\u0430\u043d\u0441\u043a\u0438, \u0402. (1994). \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u043e-\u0440\u0430\u0447\u0443\u043d\u0430\u0440\u0441\u043a\u0438 \u0441\u043e\u0444\u0442\u0432\u0435\u0440. \u0417\u0440\u0435\u045a\u0430\u043d\u0438\u043d: \u0422\u0435\u0445\u043d\u0438\u0447\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>\n
National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.<\/p>\n
Piaget, J. & Inhelder, B. (1967). The child\u2019s conception of space. New York: Norton.<\/p>\n
Plowman, L. & Stephen, C. (2005). Children, Play and Computers in Preschool Education. British Journal of Educational Technology, 36, 145\u2013157.<\/p>\n
\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \u043f\u043b\u0430\u043d\u0443 \u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u0438 \u0443\u0447\u0435\u045a\u0430 \u0437\u0430 \u0434\u0440\u0443\u0433\u0438 \u0440\u0430\u0437\u0440\u0435\u0434 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u045a\u0430 \u0438 \u0432\u0430\u0441\u043f\u0438\u0442\u0430\u045a\u0430 (2018). \u041f\u0440\u043e\u0441\u0432\u0435\u0442\u043d\u0438 \u0433\u043b\u0430\u0441\u043d\u0438\u043a, \u0421\u043b\u0443\u0436\u0431\u0435\u043d\u0438 \u0433\u043b\u0430\u0441\u043d\u0438\u043a \u0420\u0435\u043f\u0443\u0431\u043b\u0438\u043a\u0435 \u0421\u0440\u0431\u0438\u0458\u0435 \u0431\u0440. 16\/2018.<\/p>\n
\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \u043f\u043b\u0430\u043d\u0443 \u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u0438 \u0443\u0447\u0435\u045a\u0430 \u0437\u0430 \u0442\u0440\u0435\u045b\u0438 \u0440\u0430\u0437\u0440\u0435\u0434 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u045a\u0430 \u0438 \u0432\u0430\u0441\u043f\u0438\u0442\u0430\u045a\u0430 (2019). \u041f\u0440\u043e\u0441\u0432\u0435\u0442\u043d\u0438 \u0433\u043b\u0430\u0441\u043d\u0438\u043a, \u0421\u043b\u0443\u0436\u0431\u0435\u043d\u0438 \u0433\u043b\u0430\u0441\u043d\u0438\u043a \u0420\u0435\u043f\u0443\u0431\u043b\u0438\u043a\u0435 \u0421\u0440\u0431\u0438\u0458\u0435 \u0431\u0440. 5\/2019.<\/p>\n
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Yeo, J. K. K. (2008). Teaching area and perimeter: Mathematics-pedagogical-content knowledge-in-action. In G. Merrilyn, B. Ray & M. Katie (\u0435ds.): Navigating currents and charting directions: Proceedings of the 31st annual Conference of the Mathematics Education Research Group of Australasia, University of Queensland, Brisbane 28th June-1st July 2008 (621\u2013627). Adelaide, S. A.: Mathematics Education Research Group of Australasia.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"
\u041f\u0440\u0435\u0443\u0437\u043c\u0438\u0442\u0435 \u043a\u043e\u043c\u043f\u043b\u0435\u0442\u0430\u043d \u0440\u0430\u0434\/Download \u0410\u0443\u0442\u043e\u0440\u0438: \u041c\u0438\u043b\u0430\u043d \u041f. \u041c\u0438\u043b\u0438\u043a\u0438\u045b, \u0421\u0430\u045a\u0430 \u041c. \u041c\u0430\u0440\u0438\u0447\u0438\u045b, \u041d\u0435\u043d\u0430\u0434 \u0420. \u0412\u0443\u043b\u043e\u0432\u0438\u045b DOI 10.5937\/ZRPFU2224127M \u0423\u0414\u041a 37.091.39:004.4 \u041f\u0440\u0438\u043c\u0435\u043d\u0430 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 GeoGebra \u043f\u0440\u0438 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u045a\u0443 \u043f\u043e\u0458\u043c\u0430 \u043e\u0431\u0438\u043c\u0430 \u0444\u0438\u0433\u0443\u0440\u0435 \u0443 \u043c\u043b\u0430\u0452\u0438\u043c \u0440\u0430\u0437\u0440\u0435\u0434\u0438\u043c\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435 \u0410\u043f\u0441\u0442\u0440\u0430\u043a\u0442: \u0411\u0440\u043e\u0458\u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u0438\u0441\u0442\u0440\u0430\u0436\u0438\u0432\u0430\u045a\u0430 \u043f\u043e\u00ad\u043a\u0430\u0437\u0430\u043b\u0430 \u0441\u0443 \u043f\u0440\u0435\u0434\u043d\u043e\u0441\u0442\u0438 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u0438\u0445 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u0408\u0435\u0434\u0430\u043d \u043e\u0434 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043a\u0438\u0445 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u043d\u0438\u0445 \u0441\u043e\u0444\u0442\u0432\u0435\u0440\u0430 \u043a\u043e\u0458\u0438 \u0458\u0435 \u0443 \u043f\u043e\u0441\u043b\u0435\u0434\u045a\u0435 \u0432\u0440\u0435\u043c\u0435 \u0441\u0442\u0435\u043a\u0430\u043e \u0432\u0435\u043b\u0438\u043a\u0443… Read More »24 8<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/template-pagebuilder-full-width.php","meta":{"neve_meta_sidebar":"full-width","neve_meta_container":"","neve_meta_enable_content_width":"on","neve_meta_content_width":100,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"class_list":["post-1590","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/1590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1590"}],"version-history":[{"count":10,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/1590\/revisions"}],"predecessor-version":[{"id":1788,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/1590\/revisions\/1788"}],"wp:attachment":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}