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ϒ"Jԧ< ;b""jܢF[x	,!qқ*]/؝27SMcs"ޭDQ/应ܢF_!:s"7`F+SVTn"IJnQ/应B4	wD"IJ׭-`S9DrjiEJ߅gJ应矁[xZM~n"IB؃!'Тѕ+(mIKʭ/|ϐܢF[xZMzG %嬩/c[[<RI::cMΎ:z졾ܢF[RZM~D{"id":810,"date":"2021-12-20T12:26:53","date_gmt":"2021-12-20T10:26:53","guid":{"rendered":"https:\/\/zbornikradova.pfu.kg.ac.rs\/?page_id=810"},"modified":"2021-12-28T11:27:41","modified_gmt":"2021-12-28T09:27:41","slug":"23-7-2","status":"publish","type":"page","link":"https:\/\/zbornikradova.pfu.kg.ac.rs\/?page_id=810","title":{"rendered":"23 8"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"810\" class=\"elementor elementor-810\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bef2a01 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bef2a01\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bfa00d6\" data-id=\"bfa00d6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0e51a21 elementor-widget elementor-widget-text-editor\" data-id=\"0e51a21\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><br><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a href=\"https:\/\/zbornikradova.pfu.kg.ac.rs\/wp-content\/uploads\/2021\/12\/23-08-Sanja-Maricic-Jelena-Stojkanovic-U.pdf\">\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<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0410\u0443\u0442\u043e\u0440\/Authors: \u0421\u0430\u045a\u0430 \u041c. \u041c\u0430\u0440\u0438\u0447\u0438\u045b,&nbsp;<span style=\"text-indent: 0mm; color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); letter-spacing: 0px;\">\u0408\u0435\u043b\u0435\u043d\u0430 \u0420. \u0421\u0442\u043e\u0458\u043a\u0430\u043d\u043e\u0432\u0438\u045b<\/span><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><span lang=\"EN-GB\">DOI : <a href=\"https:\/\/doi.org\/10.5937\/ZRPFU2123111M\">10.5937\/ZRPFU2123111M&nbsp;<\/a><\/span><br><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0423\u0414\u041a: 37.091.3::51<\/p>\n<p><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><br><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0422\u0410\u0427\u041a\u0410\u0421\u0422\u0410 \u0418 \u041a\u0412\u0410\u0414\u0420\u0410\u0422\u041d\u0410 \u041c\u0420\u0415\u0416\u0410 \u0423 \u041d\u0410\u0421\u0422\u0410\u0412\u0418 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0408\u0415 \u0423 \u041c\u041b\u0410\u0402\u0418\u041c \u0420\u0410\u0417\u0420\u0415\u0414\u0418\u041c\u0410 \u041e\u0421\u041d\u041e\u0412\u041d\u0415 \u0428\u041a\u041e\u041b\u0415<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0410\u043f\u0441\u0442\u0440\u0430\u043a\u0442: \u0420\u0430\u0434 \u0438\u043c\u0430 \u0437\u0430 \u0446\u0438\u0459 \u0434\u0430 \u0438\u0441\u0442\u0430\u043a\u043d\u0435 \u043f\u0440\u0435\u0434\u043d\u043e\u0441\u0442 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0430 \u0442\u0430\u0447\u043a\u0430\u0441\u0442\u0435 \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0435 \u043c\u0440\u0435\u0436\u0435 \u043a\u0430\u043e \u043f\u043e\u043c\u043e\u045b\u043d\u043e\u0433 \u0430\u043b\u0430\u0442\u0430 \u0443 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0458\u0438 \u043f\u0440\u0438 \u0443\u0441\u0432\u0430\u0458\u0430\u045a\u0443 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0445 \u043f\u043e\u0458\u043c\u043e\u0432\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u045a\u0443 \u0437\u0430\u0434\u0430\u0442\u0430\u043a\u0430 \u0438\u0437 \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. \u0412\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0458\u0430 \u0458\u0435 \u0432\u0430\u0436\u0430\u043d \u0434\u0435\u043e \u043a\u043e\u0433\u043d\u0438\u0442\u0438\u0432\u043d\u043e\u0433 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438, \u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0430 \u0438 \u0442\u0430\u0447\u043a\u0430\u0441\u0442\u0430 \u043c\u0440\u0435\u0436\u0430 \u043f\u043e\u043c\u0430\u0436\u0443 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u043c\u0430 \u0434\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043a\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0443\u0458\u0443 \u0438 \u0437\u0431\u043e\u0433 \u0442\u043e\u0433\u0430 \u0441\u0443 \u0437\u043d\u0430\u0447\u0430\u0458\u043d\u0435. \u0418\u0430\u043a\u043e \u0441\u0435 \u043a\u043e\u0440\u0438\u0441\u0442\u0435 \u0443 \u0441\u0432\u0430\u043a\u043e\u043c \u043e\u0434 \u043f\u0440\u0432\u0430 \u0447\u0435\u0442\u0438\u0440\u0438 \u0440\u0430\u0437\u0440\u0435\u0434\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435 \u043f\u0440\u0438 \u043e\u0431\u0440\u0430\u0434\u0438 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u0438\u0445 \u0442\u0435\u043c\u0430 \u0438\u0437 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u043d\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438, \u0430 \u043d\u0438 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u0438\u0446\u0438 \u043d\u0435 \u043a\u043e\u0440\u0438\u0441\u0442\u0435 \u045a\u0438\u0445\u043e\u0432\u0435 \u043f\u0440\u0435\u0434\u043d\u043e\u0441\u0442\u0438 \u0443 \u0434\u043e\u0432\u043e\u0459\u043d\u043e\u0458 \u043c\u0435\u0440\u0438. \u041f\u0440\u0435\u0434\u043d\u043e\u0441\u0442 \u045a\u0438\u0445\u043e\u0432\u043e\u0433 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0430 \u043f\u043e\u0442\u0432\u0440\u0434\u0438\u043b\u0438 \u0441\u043c\u043e \u0438\u0441\u0442\u0440\u0430\u0436\u0438\u0432\u0430\u045a\u0435\u043c \u043a\u043e\u0458\u0435 \u0458\u0435 \u0441\u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e \u0441\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u043c\u0430 \u0434\u0440\u0443\u0433\u043e\u0433 \u0438 \u0447\u0435\u0442\u0432\u0440\u0442\u043e\u0433 \u0440\u0430\u0437\u0440\u0435\u0434\u0430 \u0438\u0437 \u0434\u0432\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u0435 \u0448\u043a\u043e\u043b\u0435. \u0410\u043d\u0430\u043b\u0438\u0437\u043e\u043c \u0434\u043e\u0431\u0438\u0458\u0435\u043d\u0438\u0445 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0430 \u0442\u0435\u0441\u0442\u0438\u0440\u0430\u045a\u0435\u043c \u0437\u0430\u043a\u0459\u0443\u0447\u0438\u043b\u0438 \u0441\u043c\u043e \u0434\u0430 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0435 \u043c\u0440\u0435\u0436\u0435 \u043f\u043e\u0432\u0435\u045b\u0430\u0432\u0430 \u0443\u0441\u043f\u0435\u0448\u043d\u043e\u0441\u0442 \u0440\u0435\u0448\u0430\u0432\u0430\u045a\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430. \u0421 \u043e\u0431\u0437\u0438\u0440\u043e\u043c \u043d\u0430 \u0442\u043e \u0434\u0430 \u0441\u0435 \u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043a\u043e\u0440\u0438\u0441\u0442\u0435 \u0441\u0432\u0435\u0441\u043a\u0435 \u0441\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c \u043c\u0440\u0435\u0436\u043e\u043c \u0442\u0440\u0435\u0431\u0430 \u0458\u0435 \u0438\u0441\u043a\u043e\u0440\u0438\u0441\u0442\u0438\u0442\u0438 \u043f\u043e\u0441\u0435\u0431\u043d\u043e \u0443 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435. \u0423\u0447\u0435\u043d\u0438\u0446\u0438 \u043d\u0435\u043c\u0430\u0458\u0443 \u043d\u0430\u0432\u0438\u043a\u0443 \u0434\u0430 \u0441\u0430\u043c\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0441\u043a\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0441\u043b\u0438\u043a\u043e\u043c \u043f\u0430 \u0431\u0438 \u0443\u0447\u0438\u0442\u0435\u0459\u0438 \u0442\u0440\u0435\u0431\u0430\u043b\u043e \u043d\u0430 \u0442\u043e\u043c\u0435 \u0434\u0430 \u0438\u043d\u0441\u0438\u0441\u0442\u0438\u0440\u0430\u0458\u0443.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u041a\u0459\u0443\u0447\u043d\u0435 \u0440\u0435\u0447\u0438: \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0458\u0430, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0430 \u043c\u0440\u0435\u0436\u0430, \u0442\u0430\u0447\u043a\u0430\u0441\u0442\u0430 \u043c\u0440\u0435\u0436\u0430, \u0433\u0435\u043e\u0442\u0430\u0431\u043b\u0430, \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0430.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a><\/a><a><\/a>&nbsp;<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">DOTTED GRID AND SQUARE GRID IN TEACHING GEOMETRY IN LOWER GRADES OF ELEMENTARY SCHOOL<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Abstract: This work aims to underline the advantage of use of dotted grid and square grid as auxiliary tools for visualization in adoption of basic notions in geometry and problems solving in geometry in lower grades of elementary school. Visualization is an important part of cognitive process in mathematics while square grid and dotted grid help students visualize mathematic tasks therefore being significant. Although they are used in every grade of the initial four grades of primary school in the process of teaching geometry topics, neither students nor teachers use their advantages to a sufficient extent. The advantages of their use have been confirmed in the research conducted with the students of second and fourth grade in two primary schools. By analyzing of the obtained test results, we concluded that the use of the square grid increases the success in problem solving. Considering that notebooks with a square grid are used in mathematics teaching, the square grid should be used especially in the field of geometry.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Keywords: visualization, square grid, dotted grid, geoboard, geometry.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><br><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u041b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430\/<span style=\"color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); letter-spacing: 0px;\">References<\/span><span style=\"text-indent: 0mm; color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); letter-spacing: 0px;\">:<\/span><\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Abonyi, O. &amp; Eze, A. (2006). Effect of Geoboard on junior secondary school students\u2019 achievement in geometry. Ebonyi State University Journal of Education (EBJE), 4, 243\u2013250.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215\u2013241.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Bishop, A. (1989). Review of research in visualization in mathematics education. Focus on Learning Problems in Mathematics, 11(1), 7\u201316.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Boggan, M., Harper, S. &amp; Whitmire, A. (2010). Using Manipulatives to Teach Elementary Mathematics.&nbsp;Journal of Instructional Pedagogies,&nbsp;3, 1\u20136.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Vlasnovi\u0107, H. i Cindri\u0107, M. (2014). Razumevanje geometrijskih pojmova i razvitak geometrijskog mi\u0161ljenja u\u010denika ni\u017eih razreda osnovne \u0161kole prema Van Hileovoj teoriji. \u0160kolski vjesnik, 63(1\u20132), 37\u201351.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Guncaga, J. &amp; \u017dilkov\u00e1, K. (2019). Visualisation as a Method for the Development of the Term Rectangle for Pupils in Primary School. European Journal of Contemporary Education, 8(1), 52\u201368.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0414\u0430\u043b\u0438\u043d\u0433\u0435\u0440, \u0412. \u0410. \u0438 \u041a\u043d\u044f\u0437\u0435\u0432\u0430 \u041e. \u041e. (2004). \u041a\u043e\u0433\u043d\u0438\u0442\u0438\u0432\u043d\u043e-\u0432\u0438\u0437\u0443\u0430\u043b\u044c\u043d\u044b\u0439 \u043f\u043e\u0434\u0445\u043e\u0434 \u043a \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u041e\u043c\u0441\u043a: \u041e\u043c\u0413\u041f\u0423.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Duval, R. (1998). Geometry from the cognitive point of view. In C. Mammana &amp; V. Villani (eds.). Perspectives on the Teaching of Geometry for the 21st Century, \u0430n ICMI Study (37\u201352). Kluwer Academic Publishers.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0402\u043e\u043a\u0438\u045b, \u041e. (2013). \u0420\u0435\u0430\u043b\u043d\u043e \u043e\u043a\u0440\u0443\u0436\u0435\u045a\u0435 \u0443 \u043f\u043e\u0447\u0435\u0442\u043d\u043e\u0458 \u043d\u0430\u0441\u0442\u0430\u0432\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435. (\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). \u0411\u0435\u043e\u0433\u0440\u0430\u0434: \u0423\u0447\u0438\u0442\u0435\u0459\u0441\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0402\u043e\u043a\u0438\u045b, \u041e. \u0438 \u0417\u0435\u0459\u0438\u045b, \u041c. (2017). \u0422\u0435\u043e\u0440\u0438\u0458\u0435 \u0440\u0430\u0437\u0432\u043e\u0458\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0441\u043a\u043e\u0433 \u043c\u0438\u0448\u0459\u0435\u045a\u0430 \u043f\u0440\u0435\u043c\u0430 \u0412\u0430\u043d \u0425\u0438\u043b\u0443, \u0424\u0438\u0448\u0431\u0430\u0458\u043d\u0443 \u0438 \u0423\u0434\u0435\u043c\u043e\u043d-\u041a\u0443\u0437\u043d\u0438\u0430\u043a\u0443. \u0422\u0435\u043c\u0435, 41(3), 623\u2013637.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Jones, K. (2002). Issues in the teaching and learning of geometry. In L. Haggarty (\u0435d.): Aspects of Teaching Secondary Mathematics: perspectives on practice (121\u2013139). London: Routledge.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u041a\u043e\u0441\u0442\u0438\u045b, \u0412. \u0421\u0435\u043a\u0443\u043b\u0438\u045b, \u0422. \u0438 \u0421\u0442\u0430\u043d\u043a\u043e\u0432\u0438\u045b-\u0402\u043e\u0440\u0452\u0435\u0432\u0438\u045b, \u041c. (2014). \u0424\u043e\u0440\u043c\u0438\u0440\u0430\u045a\u0435 \u043f\u043e\u0447\u0435\u0442\u043d\u0438\u0445 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043a\u0438\u0445 \u043f\u043e\u0458\u043c\u043e\u0432\u0430 \u2013 \u043e\u0434 \u0432\u0438\u0437\u0443\u0435\u043b\u043d\u043e\u0433 \u0434\u043e \u0441\u0438\u043c\u0431\u043e\u043b\u0438\u0447\u043a\u043e\u0433. \u0423 \u0414. \u0412\u0438\u0434\u0430\u043d\u043e\u0432\u0438\u045b (\u0443\u0440.): \u0425\u043e\u043b\u0438\u0441\u0442\u0438\u0447\u043a\u0438 \u043f\u0440\u0438\u0441\u0442\u0443\u043f \u0443 \u043f\u0440\u0435\u0434\u0448\u043a\u043e\u043b\u0441\u043a\u043e\u0458 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0458\u0438 \u2013 \u0442\u0435\u043e\u0440\u0438\u0458\u0430 \u0438 \u043f\u0440\u0430\u043a\u0441\u0430, \u0417\u0431\u043e\u0440\u043d\u0438\u043a \u0440\u0430\u0434\u043e\u0432\u0430 \u0434\u0440\u0443\u0433\u043e\u0433 \u0441\u0442\u0440\u0443\u0447\u043d\u043e-\u043d\u0430\u0443\u0447\u043d\u043e\u0433 \u0441\u043a\u0443\u043f\u0430 \u0441\u0430 \u043c\u0435\u0452\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u043c \u0443\u0447\u0435\u0448\u045b\u0435\u043c \u0425\u041e\u041b\u0418\u041f\u0420\u0418 2014 (188\u2013199). \u041f\u0438\u0440\u043e\u0442: \u0412\u0438\u0441\u043e\u043a\u0430 \u0448\u043a\u043e\u043b\u0430 \u0441\u0442\u0440\u0443\u043a\u043e\u0432\u043d\u0438\u0445 \u0441\u0442\u0443\u0434\u0438\u0458\u0430 \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u045a\u0435 \u0432\u0430\u0441\u00ad\u043f\u0438\u0442\u0430\u0447\u0430.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u041c\u0438\u043b\u0438\u043d\u043a\u043e\u0432\u0438\u045b, \u0408. \u0438 \u041c\u0438\u045b\u0438\u045b, \u0412. (2008). \u0423\u043b\u043e\u0433\u0430 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u043a\u0438\u0445 \u0441\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0430 \u0443 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0448\u043a\u043e\u043b\u00ad\u0441\u043a\u043e\u0458 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0438. \u0423 \u041c. \u0415\u0433\u0435\u0440\u0438\u045b (\u0443\u0440.): \u041c\u0435\u0442\u043e\u0434\u0438\u0447\u043a\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u00ad\u0442\u0438\u043a\u0435 (33\u201337). \u0408\u0430\u0433\u043e\u0434\u0438\u043d\u0430: \u041f\u0435\u0434\u0430\u0433\u043e\u0448\u043a\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0435\u0442.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a><\/a><a><\/a>\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u0438 \u0443\u0447\u0435\u045a\u0430 \u0437\u0430 \u043f\u0440\u0432\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\u00ad\u043f\u0438\u0442\u0430\u045a\u0430 (2017). \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. 10\/2017-1.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a><\/a>\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \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\/2018-47.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \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\/2019-6.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a><\/a><a><\/a>\u041f\u0440\u0430\u0432\u0438\u043b\u043d\u0438\u043a \u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443 \u043d\u0430\u0441\u0442\u0430\u0432\u0435 \u0438 \u0443\u0447\u0435\u045a\u0430 \u0437\u0430 \u0447\u0435\u0442\u0432\u0440\u0442\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. 11\/2019\u20131.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u0420\u0430\u043a\u043e\u045a\u0430\u0446, \u041c. \u0438 \u041c\u0438\u043b\u0438\u043d\u043a\u043e\u0432\u0438\u045b, \u0408. (2019). \u0423\u0442\u0438\u0446\u0430\u0458 \u043f\u0440\u0438\u043c\u0435\u043d\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0442\u0438\u0445 \u0440\u0435\u043f\u0440\u0435\u0437\u0435\u043d\u0442\u0430\u0446\u0438\u0458\u0430 \u043f\u043e\u0458\u043c\u043e\u0432\u0430 \u0438 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430 \u043d\u0430 \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0443\u0430\u043b\u043d\u043e \u0440\u0430\u0437\u0443\u043c\u0435\u0432\u0430\u045a\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, 22(21), 207\u2013226.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Rahmiati, M. (2016). The attempt to improve mathematics learning motivation using the geoboard (Spiked Board). Among Grade II Elementary School Students. Global Journal of Business and Social Science Review, 4(3), 74\u201378.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">R\u00f6sken, B. &amp; Rolka, K. (2006). A picture is worth a 1000 words \u2013 the role of &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;visualization in mathematics learning. In J. Novotna\u0301, H. Moraova\u0301, M. Kra\u0301tka\u0301 &amp; N. Stehli\u0301kova\u0301 (eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, 457\u2013464. Prague: PME.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Sani, S. &amp; Salahudeen, B. (2016). Effects of Geoboard and geographical globe on senior secondary school students\u2019 performance in mathematics in Kaduna state. Journal of Science, Technology &amp; Education, 4(1), 140\u2013148.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Sibiya, M. R. (2019). The effect of Geoboard use on learners\u2019 motivation for learning of Geometry theorems. International Journal of Sciences and Research, 75(6), 71\u201385, <a href=\"https:\/\/doi.org\/10.21506\/j.ponte.2019.6.14\">https:\/\/doi.org\/10.21506\/j.ponte.2019.6.14<\/a>.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Sibiya, M. R. (2020). A Reconsideration of the Effectiveness of Using Geoboard in Teaching Euclidean Geometry. EURASIA Journal of Mathematics, Science and Technology Education, 16(9), 1\u201310, <a href=\"https:\/\/doi.org\/10.29333\/ejmste\/8360\">https:\/\/doi.org\/10.29333\/ejmste\/8360<\/a>.&nbsp;<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\"><a><\/a>\u0421\u0442\u0430\u043d\u043e\u0458\u0435\u0432\u0438\u045b, \u0414. \u0438 \u041c\u0438\u043b\u0438\u043d\u043a\u043e\u0432\u0438\u045b, \u0408. (2013). \u0422\u0418\u041c\u0421\u0421 2011-\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u043f\u0440\u0435\u0433\u043b\u0435\u0434 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u043e\u0433 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u0438 \u0437\u0431\u0438\u0440\u043a\u0430 \u0437\u0430\u0434\u0430\u0442\u0430\u043a\u0430 \u0437\u0430 4. \u0440\u0430\u0437\u0440\u0435\u0434. \u0411\u0435\u043e\u0433\u0440\u0430\u0434: \u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0437\u0430 \u043f\u0435\u0434\u0430\u0433\u043e\u0448\u043a\u0430 \u0438\u0441\u0442\u0440\u0430\u0436\u0438\u0432\u0430\u045a\u0430.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Seefeldt, C. &amp; Wasik, B. A. (2006). Early education: three-, four-, and five-year-olds go to School (2nd ed.). Upper Saddle River: Pearson Education.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Scandrett, H. (2008). Using Geoboards in Primary Mathematics: Going&#8230; Going&#8230; Gone?.&nbsp;Australian Primary Mathematics Classroom,&nbsp;13(2), 29\u201332.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Stylianou, D. A. &amp; Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences. Mathematical Thinking and Learning, 6(4), 353\u2013387.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Fischbein, E. (1977). Image and concept in learning mathematics. Educational Studies in Mathematics, 8, 153\u2013165.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Freudenthal, H. (1973). Mathematics as an educational task. Netherlands: Reidel Publishing Company, Dordrecht\u2212Holland.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Freire, A. F., Rodrigues, F. S., Aquino, M. R., Soares, M. V., Gois, D. D. &amp; Viana, J. D. (2018). The use of the Geoboard in teaching Geometry: calculating area and perimeter. Multidisciplinary Core scientific journal of knowledge, 3, 119\u2013135.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">Furner, J. M. &amp; Marinas, C. A. (2011). Geoboards to GeoGebra: Moving from the concrete 6 to the abstract in geometry. Retri\u0435ved June 19, 2021 from the World Wide Web <a href=\"http:\/\/archives.math.utk.edu\/ICTCM\/VOL23\/S0%2088\/paper.pdf\">http:\/\/archives.math.utk.edu\/ICTCM\/VOL23\/S0 88\/paper.pdf<\/a><a><\/a>.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\u010ci\u017eme\u0161ija, \u0410. Soucie, T. &amp; Svedrec, R. (2012). Primjena geoplo\u010de u nastavi matematike.&nbsp; Pou\u010dak: \u010dasopis za metodiku i nastavu matematike, 50, 25\u201339.<\/p>\n<p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/p><p style=\"margin-left: 10.0mm; text-indent: 0mm;\">\n<\/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":"<p>\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\/Authors: \u0421\u0430\u045a\u0430 \u041c. \u041c\u0430\u0440\u0438\u0447\u0438\u045b,&nbsp;\u0408\u0435\u043b\u0435\u043d\u0430 \u0420. \u0421\u0442\u043e\u0458\u043a\u0430\u043d\u043e\u0432\u0438\u045b DOI : 10.5937\/ZRPFU2123111M&nbsp; \u0423\u0414\u041a: 37.091.3::51 \u0422\u0410\u0427\u041a\u0410\u0421\u0422\u0410 \u0418 \u041a\u0412\u0410\u0414\u0420\u0410\u0422\u041d\u0410 \u041c\u0420\u0415\u0416\u0410 \u0423 \u041d\u0410\u0421\u0422\u0410\u0412\u0418 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0408\u0415 \u0423 \u041c\u041b\u0410\u0402\u0418\u041c \u0420\u0410\u0417\u0420\u0415\u0414\u0418\u041c\u0410 \u041e\u0421\u041d\u041e\u0412\u041d\u0415 \u0428\u041a\u041e\u041b\u0415 \u0410\u043f\u0441\u0442\u0440\u0430\u043a\u0442: \u0420\u0430\u0434 \u0438\u043c\u0430 \u0437\u0430 \u0446\u0438\u0459 \u0434\u0430 \u0438\u0441\u0442\u0430\u043a\u043d\u0435 \u043f\u0440\u0435\u0434\u043d\u043e\u0441\u0442 \u043a\u043e\u0440\u0438\u0448\u045b\u0435\u045a\u0430 \u0442\u0430\u0447\u043a\u0430\u0441\u0442\u0435 \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0435 \u043c\u0440\u0435\u0436\u0435 \u043a\u0430\u043e \u043f\u043e\u043c\u043e\u045b\u043d\u043e\u0433 \u0430\u043b\u0430\u0442\u0430 \u0443 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0458\u0438 \u043f\u0440\u0438 \u0443\u0441\u0432\u0430\u0458\u0430\u045a\u0443 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0445 \u043f\u043e\u0458\u043c\u043e\u0432\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u045a\u0443 \u0437\u0430\u0434\u0430\u0442\u0430\u043a\u0430 \u0438\u0437 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0458\u0435 \u0443&hellip;&nbsp;<a href=\"https:\/\/zbornikradova.pfu.kg.ac.rs\/?page_id=810\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">23 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-810","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/810","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=810"}],"version-history":[{"count":14,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/810\/revisions"}],"predecessor-version":[{"id":1126,"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=\/wp\/v2\/pages\/810\/revisions\/1126"}],"wp:attachment":[{"href":"https:\/\/zbornikradova.pfu.kg.ac.rs\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}