{"id":41082,"date":"2016-08-08T20:59:00","date_gmt":"2016-08-08T17:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016\/mathinfocontent042016\/"},"modified":"2019-06-18T21:58:29","modified_gmt":"2019-06-18T18:58:29","slug":"mathinfocontent042016","status":"publish","type":"post","link":"https:\/\/strategies.azbuki.bg\/en\/matematics\/matharticles2016\/mathinfocontent042016\/","title":{"rendered":"Mathematics and Informatics, Number 4\/2016, Volume 59"},"content":{"rendered":"<p><strong><a name=\"top\"><br \/> <\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL MATTERS\/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><\/p>\n<p><a href=\"#art01\"> \u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0414\u0440\u043e\u0437-\u0424\u0430\u0440\u043d\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043e \u043e\u0442 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 <br \/>[Generalization of Droz-Farny Theorem Defined by a Circum-conic] <\/a>\/ <br \/>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov &ndash; \u0441\u0442\u0440. 351<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_SavaGrozdev_VeselinNenkov.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art02\"> \u0410\u043a\u0442\u0438\u0432\u043d\u043e, \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0449\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 &ndash; \u0442\u0438\u043f \u0438\u043d\u0442\u0435\u0440\u0432\u044e <br \/>[In-depth Interview] <\/a>\/ <br \/>\u0425\u0440\u0438\u0441\u0442\u043e \u0425\u0440\u0438\u0441\u0442\u043e\u0432, \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432 \/ Hristo Hristov, Hristo Krushkov &#8211; \u0441\u0442\u0440. 368<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_HristoHristov_HristoKrushkov.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONALTECHNOLOGIES \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong><\/p>\n<p><a href=\"#art03\"> \u0425\u0438\u043f\u043e\u0442\u0435\u0437\u0430\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <br \/>[The Hypothesis in Teaching Mathematics] <\/a>\/ <br \/>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430 \/ Rumyana Mavrova, Penka Rangelova, Elena Todorova &#8211; \u0441\u0442\u0440. 381<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_Mavrova_Rangelova_Todorova.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art04\">Comparative Analysis of the Students&rsquo; Scores in Solving Constructive Tasks <br \/>when Geometry is Studied in a Standard Way and with the Use of Complex Numbers <\/a>\/<br \/> Katerina Anevska, Risto Malceski, Metodi Glavche &#8211; \u0441\u0442\u0440. 391<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_KaterinaAnevska_MetodiGlavche_RistoMalceski.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art05\"> \u041f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 \u0442\u0438\u043f Pisa, \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u0437\u0430 \u043e\u0431\u0449\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435<br \/> [ApracticalProblemofPisaTypeStudiedbySoftwareforGeneralApplication]<\/a> \/<br \/> \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u0441\u0438\u0441\u043b\u0430\u0432\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430 \/ Sava Grozdev, Desislava Georgieva &#8211; \u0441\u0442\u0440. 402<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_SavaGrozdev_DesislavaGeorgieva.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art06\"> \u041e\u0442 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u043e \u043a\u044a\u043c \u043e\u0431\u0435\u043a\u0442\u043d\u043e-\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 <br \/>[FromStructuredtoObject-orientedProgramming] <\/a>\/ <br \/>\u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432 \/ HristoKrushkov &#8211; \u0441\u0442\u0440. 416<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_HristoKrushkov.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art07\"> \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u0442\u0435 \u0438\u0433\u0440\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 &#8211; \u043f\u0440\u0435\u0434\u0438\u0437\u0432\u0438\u043a\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438<br \/> [ComputerGamesinMathematicsEducation- ChallengesandOpportunities] <\/a>\/ <br \/>\u041c\u0430\u044f \u0421\u0442\u043e\u044f\u043d\u043e\u0432\u0430, \u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0414\u0443\u0440\u0435\u0432\u0430-\u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430, \u041a\u043e\u0441\u0442\u0430\u0434\u0438\u043d \u0421\u0430\u043c\u0430\u0440\u0434\u0436\u0438\u0435\u0432 \/ <br \/>MayaStoyanova, Daniela Dureva-Tuparova, Kostadin Samardzhiev &#8211; \u0441\u0442\u0440. 432<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_Stoyanova_Dureva-Tuparova_Samardzhiev.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>CONTEST PROBLEMS\/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>Contest Problems of this Issue <br \/>[Contest Problems of this Issue] &#8211; \u0441\u0442\u0440. 446<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_KonkursniZadachi.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 5, 2015 <br \/>[Solutions of the Contest Problems from Issue 5, 2015] &#8211; \u0441\u0442\u0440. 447<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/09\/azbuki.bg_dmdocuments_Matematika_0416_reshenia.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>READ IN THE LATEST ISSUES OF&bdquo;AZBUKI&ldquo; JOURNALS \/<br \/> \u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e &bdquo;\u0410\u0417-\u0411\u0423\u041a\u0418&ldquo; \u0427\u0415\u0422\u0415\u0422\u0415 &#8211; \u0441\u0442\u0440. 451<\/p>\n<p>&nbsp;<\/p>\n<p>GUIDEFORAUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 &#8211; \u0441\u0442\u0440. 453<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art01\"><\/a> \u041e\u0411\u041e\u0411\u0429\u0415\u041d\u0418\u0415 \u041d\u0410 \u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u041d\u0410 \u0414\u0420\u041e\u0417-\u0424\u0410\u0420\u041d\u0418, \u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u041e \u041e\u0422 \u041e\u041f\u0418\u0421\u0410\u041d\u041e \u041a\u041e\u041d\u0418\u0427\u041d\u041e \u0421\u0415\u0427\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Sava Grozdev<\/strong><\/p>\n<p>VUZF University<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong><\/p>\n<p>\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 &ndash; \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412\u044a\u0432 \u0432\u0440\u044a\u0437\u043a\u0430 \u0441 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0442\u0435 \u0437\u0430 \u0434\u0430\u0434\u0435\u043d \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a ABC \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0435 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0435\u043d\u043e \u0435\u0434\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430 \u0414\u0440\u043e\u0437-\u0424\u0430\u0440\u043d\u0438. \u041e\u043f\u0438- \u0441\u0430\u043d\u043e\u0442\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0435 \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u043e \u0441\u044a\u0441 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u0438 \u0432\u043f\u0438\u0441\u0430\u043d\u0438 \u0437\u0430 &ugrave; &Delta; \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435&shy;\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p>Keywords: triangle, conic, Euler circle, Euler line, conjugate line<\/p>\n<p>&nbsp;<\/p>\n<p><strong>GENERALIZATION OF DROZ-FARNY THEOREM DEFINED BY A CIRCUM-CONIC<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. A generalization of a well-known theorem of Droz-Farny is established concerning the circum-conics of a given triangle ABC . The described generalization is connected with special circum-conics of ABC &Delta;.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Sava Grozdev<\/strong><\/p>\n<p>University of Finance, Business and Entrepreneurship<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Veselin Nenkov<\/strong><\/p>\n<p>Technical College Lovech<\/p>\n<hr \/>\n<p><strong><a name=\"art02\"><\/a> \u0410\u041a\u0422\u0418\u0412\u041d\u041e, \u0423\u0427\u0410\u0421\u0422\u0412\u0410\u0429\u041e \u041d\u0410\u0411\u041b\u042e\u0414\u0415\u041d\u0418\u0415 &amp;NDASH; \u0422\u0418\u041f \u0418\u041d\u0422\u0415\u0420\u0412\u042e<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0425\u0440\u0438\u0441\u0442\u043e \u0425\u0440\u0438\u0441\u0442\u043e\u0432, \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432<\/strong><\/p>\n<p>\u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u041f. \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0432\u044a\u043f\u0440\u043e\u0441\u0438\u0442\u0435 \u0437\u0430 \u0441\u044a\u0449\u043d\u043e\u0441\u0442\u0442\u0430, \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435\u0442\u043e \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u0438\u044f \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u043c\u0435\u0442\u043e\u0434 &bdquo;\u0410\u043a\u0442\u0438\u0432\u043d\u043e, \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0449\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 &ndash; \u0442\u0438\u043f \u0438\u043d\u0442\u0435\u0440\u0432\u044e&ldquo;. \u041e\u0431\u044a\u0440\u043d\u0430\u0442\u043e \u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\u0438, \u043f\u0440\u0438 \u043a\u043e\u0438\u0442\u043e \u0437\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438\u0442\u0435 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0438\u044f \u0441\u0435 \u043d\u0430\u043b\u0430\u0433\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0442\u0434\u0435\u043b\u043d\u0438, \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0438 \u0437\u0430 \u043f\u0440\u0435\u0434\u043c\u0435\u0442\u043d\u0430\u0442\u0430 \u043e\u0431\u043b\u0430\u0441\u0442 \u043c\u0435\u0442\u043e\u0434\u0438.<\/p>\n<p>\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u0430\u0432\u0442\u043e\u0440\u0441\u043a\u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043e\u0442 \u0442\u0430\u043a\u044a\u0432 \u0442\u0438\u043f, \u043a\u043e\u0439\u0442\u043e \u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d \u043f\u0440\u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0438 \u0442\u0435\u043e\u0440\u0438\u0438 \u0437\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u0438 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0441\u044a\u0441\u0442\u043e\u044f\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438. \u0417\u0430 \u043e\u0441\u043d\u043e\u0432\u0430 \u043d\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435\u0442\u043e \u043c\u0443 \u0435 \u043f\u043e\u0441\u043b\u0443\u0436\u0438\u043b\u0430 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u0430\u0442\u0430 &bdquo;\u0422\u0435\u043e\u0440\u0438\u044f, \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0430 \u043d\u0430 \u0434\u0430\u043d\u043d\u0438&ldquo; \u043d\u0430 \u0411. \u0413\u043b\u0435\u0439\u0437\u044a\u0440 \u0438 \u0410. \u0429\u0440\u0430\u0443\u0441. \u041f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e\u043c \u043d\u0435\u044f, \u0432 &bdquo;\u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0449\u043e\u0442\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 &ndash; \u0442\u0438\u043f \u0438\u043d\u0442\u0435\u0440\u0432\u044e&ldquo;, \u0441\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430\u043d\u0438 \u043a\u043b\u044e\u0447\u043e\u0432\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438 \u043d\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u0442\u0435 &bdquo;\u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435&ldquo; \u0438 &bdquo;\u0438\u043d\u0442\u0435\u0440\u0432\u044e&ldquo;. \u0422\u043e\u0439 \u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d, \u043a\u0430\u0442\u043e \u0435\u0434\u0438\u043d \u043e\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u0442\u0435, \u043f\u043e\u0441\u043b\u0443\u0436\u0438\u043b\u0438 \u0437\u0430 \u043f\u043e\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0438 \u043d\u0430 \u0442\u0435\u043e\u0440\u0438\u044f \u043d\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430 \u043d\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438.<\/p>\n<p>Keywords: Qualitative methods, Teaching Methodology,Grounded Theory<\/p>\n<p>&nbsp;<\/p>\n<p><strong>IN-DEPTH INTERVIEW<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The article addresses the issue of the nature, development and application of qualitative research method &#8222;In-Depth Interview&#8220;. Attention is paid to the specifics of the qualitative methods in which the various studies require to develop separate, specialized research methods.<\/p>\n<p>The method of type In-Depth Interview developed by the authors is presented in the study of contemporary theories to create software and to analyse the state of education in software engineering. The qualitative &#8222;Grounded Theory&#8220; of B. Glaser and A. Strauss serves as a basis for its development. Through it, in &#8222;In-Depth Interview&#8220;, key issues are integrated like the methods &#8222;observation&#8220; and &#8222;interview&#8220;. It is one of the methods to build the foundations of the theory of teaching methodology of software engineering.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Hristo Hristov, Assist. Prof.<\/strong><\/p>\n<p><strong>Dr. Hristo Krushkov, Assoc. Prof.<\/strong><\/p>\n<p>UniversityofPlovdiv<\/p>\n<hr \/>\n<p><strong><a name=\"art03\"><\/a>\u0425\u0418\u041f\u041e\u0422\u0415\u0417\u0410\u0422\u0410 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430<\/strong><\/p>\n<p>\u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u041f\u0430\u0438\u0441\u0438\u0439 \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0441\u0435 \u043f\u043e\u043a\u0430\u0437\u0432\u0430 \u0438\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0445\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u0447\u0440\u0435\u0437 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0434\u0443\u043a\u0446\u0438\u044f \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.<\/p>\n<p>Keywords: teaching, hypothesis, analogy, induction<\/p>\n<p>&nbsp;<\/p>\n<p><strong>THE HYPOTHESIS IN TEACHING MATHEMATICS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract.&nbsp;The present paper shows the building of a hypothesis via analogy and induction in teaching Mathematics.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Rumyana Mavrova, Assoc. Prof<\/strong><\/p>\n<p><strong>Prof. Dr. Penka Rangelova<\/strong><\/p>\n<p><strong>Dr. Elena Todorova, Assist. Prof<\/strong><\/p>\n<p>Plovdiv University &ldquo;Paisiy Hilendarskiy&rdquo;<\/p>\n<hr \/>\n<p><strong><a name=\"art04\"><\/a> COMPARATIVE ANALYSIS OF THE STUDENTS&amp;RSQUO; SCORES IN SOLVING CONSTRUCTIVE TASKS <br \/>WHEN GEOMETRY IS STUDIED IN A STANDARD WAY AND WITH THE USE OF COMPLEX NUMBERS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The students learn about complex numbers and Euclidean plane geometry in high school. Nevertheless, this material is separated into units instead of being integrated. (Anevska, 2014) presents methodological aspects about the study of exponential presentation of the complex numbers and(Anevska &amp; al.2015-1) presents the possibility for inter-subject integration of the mathematics instruction in the study of the mentioned topics. Further on, (Anevska &amp; al., 2015-2) and (Anevska &amp; al., 2016) present the results of the comparative analyses of the scores of the students regarding the transformations in the Euclidean plane and the metric characteristics of the geometric figures and their use when studied in the standard way (see (Mitrovi\u0107 &amp; al., 1998)), and when studied with the use of complex numbers (see (Malcheski &amp; al., 2015)). This paper offers analogous analyses regarding the acquired knowledge in these two ways when solving constructive tasks.<\/p>\n<p>Keywords: complex number, geometric construction, test, hypothesis.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Katerina Anevska<\/strong><\/p>\n<p><strong>Prof. Risto Malceski, DSc.<\/strong><\/p>\n<p>FON University, Skopje<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Metodi Glavche<\/strong><\/p>\n<p>Cyril and Methodius University, Skopje<\/p>\n<hr \/>\n<p><strong><a name=\"art06\"><\/a> \u041f\u0420\u0410\u041a\u0422\u0418\u0427\u0415\u0421\u041a\u0410 \u0417\u0410\u0414\u0410\u0427\u0410 \u041e\u0422 \u0422\u0418\u041f PISA, \u0418\u0417\u0421\u041b\u0415\u0414\u0412\u0410\u041d\u0410 \u0421 \u041f\u041e\u041c\u041e\u0429\u0422\u0410 \u041d\u0410 \u0421\u041e\u0424\u0422\u0423\u0415\u0420 \u0417\u0410 \u041e\u0411\u0429\u041e \u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Sava Grozdev<\/strong><\/p>\n<p>VUZF University<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Desislava Georgieva<\/strong><\/p>\n<p>\u0420\u0443\u0441\u0435\u043d\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u0410\u043d\u0433\u0435\u043b \u041a\u044a\u043d\u0447\u0435\u0432&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0435\u0434\u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u0435 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0446\u0435\u043d\u0430\u0440\u0438\u0439 \u0437\u0430 \u0443\u0440\u043e\u043a \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0431\u0430\u0437\u0438\u0440\u0430\u043d \u043d\u0430 \u043c\u043d\u043e\u0433\u043e\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u0441 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0438 \u0447\u0435\u0440\u0442\u0435\u0436\u0438 \u0438 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0438.<\/p>\n<p>Keywords: mathematics, practical problem, multiple representations, spreadsheets<\/p>\n<p>&nbsp;<\/p>\n<p><strong>A PRACTICAL PROBLEM OF PISA TYPE STUDIED BY SOFTWARE FOR GENERAL APPLICATION <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The paper is dedicated to a practical problem in mathematics. A didactic scenario is proposed for a mathematical class lesson, based on a multiple representation applying dynamic drawings and spreadshe ets.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<\/strong><\/p>\n<p>University of Finance, Business and Entrepreneurship<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Ms. Desislava Georgieva, PhD student<\/strong><\/p>\n<p>University of Ruse<\/p>\n<hr \/>\n<p><strong><a name=\"art06\"><\/a>\u041e\u0422 \u0421\u0422\u0420\u0423\u041a\u0422\u0423\u0420\u041d\u041e \u041a\u042a\u041c \u041e\u0411\u0415\u041a\u0422\u041d\u041e-\u041e\u0420\u0418\u0415\u041d\u0422\u0418\u0420\u0410\u041d\u041e \u041f\u0420\u041e\u0413\u0420\u0410\u041c\u0418\u0420\u0410\u041d\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>\u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432<\/p>\n<p>\u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u041f. \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412\u044a\u0437\u043d\u0438\u043a\u043d\u0430\u043b\u043e \u0432 \u043a\u0440\u0430\u044f \u043d\u0430 \u0448\u0435\u0441\u0442\u0434\u0435\u0441\u0435\u0442\u0442\u0435 \u0433\u043e\u0434\u0438\u043d\u0438 \u043d\u0430 \u0434\u0432\u0430\u0434\u0435\u0441\u0435\u0442\u0438 \u0432\u0435\u043a, \u0443\u0442\u0432\u044a\u0440\u0434\u0438\u043b\u043e \u0441\u0435 \u043f\u0440\u0435\u0437 \u043e\u0441\u0435\u043c\u0434\u0435\u0441\u0435\u0442\u0442\u0435 \u0433\u043e\u0434\u0438\u043d\u0438 \u0438 \u043e\u0441\u043e\u0431\u0435\u043d\u043e \u0431\u0443\u0440\u043d\u043e \u0440\u0430\u0437\u0432\u0438\u043b\u043e \u0441\u0435 \u043f\u0440\u0435\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u043e\u0442\u043e \u043c\u0443 \u0434\u0435\u0441\u0435\u0442\u0438\u043b\u0435\u0442\u0438\u0435, \u043e\u0431\u0435\u043a\u0442\u043d\u043e-\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e\u0442\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 (\u041e\u041e\u041f) \u0441\u0435 \u043d\u0430\u043b\u043e\u0436\u0438 \u043a\u0430\u0442\u043e \u0432\u043e\u0434\u0435\u0449 \u0441\u0442\u0438\u043b \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0432 \u043d\u0430\u0447\u0430\u043b\u043e\u0442\u043e \u043d\u0430 \u043d\u043e\u0432\u0438\u044f \u0432\u0435\u043a. \u0418 \u0434\u043e\u043a\u0430\u0442\u043e \u0442\u043e\u0437\u0438 \u0441\u0442\u0438\u043b \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0435 \u043f\u043e\u0447\u0442\u0438 \u0431\u0435\u0437\u0430\u043b\u0442\u0435\u0440\u043d\u0430\u0442\u0438\u0432\u0435\u043d \u0432 \u043c\u0430\u0441\u043e\u0432\u043e\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440, \u0432\u043d\u0435\u0434\u0440\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043c\u0443 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0448\u043a\u043e\u043b\u0441\u043a\u0430\u0442\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430 \u0437\u0430\u043a\u044a\u0441\u043d\u044f\u0432\u0430. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0438 \u043f\u0440\u0438\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0431\u0430\u0432\u043d\u043e\u0442\u043e \u043d\u0430\u0432\u043b\u0438\u0437\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u0435\u043a\u0442\u043d\u043e-\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e\u0442\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0442\u043e \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u0438 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435\u0434\u0438\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u0441\u043c\u044f\u043d\u0430 \u043d\u0430 \u0441\u0442\u0438\u043b\u0430 \u043d\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0442\u0430 &bdquo;\u041f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435&ldquo;. \u041f\u043e\u0434\u0445\u043e\u0434\u044a\u0442 \u0435 \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u043d \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0441\u043a\u0438 \u0438\u0437\u043f\u0438\u0442 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u041f\u0423 &bdquo;\u041f\u0430\u0438\u0441\u0438\u0439 \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438&ldquo; \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0439\u043a\u0438 \u0421#.<\/p>\n<p>Keywords: computer science education, object-oriented programming, teaching programming, teaching methodology<\/p>\n<p>&nbsp;<\/p>\n<p><strong>FROM STRUCTURED TO OBJECT-ORIENTED PROGRAMMING<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. Arose in the late sixties of the twentieth century, affirmed through the eighties and especially booming in its last decade, object-oriented programming has established itself as a leading style of programming at the beginning of the new century. While this style of programming has almost no alternative in the mass production of software, its imposition in secondary school educational practice is delayed. The article analyses the reasons for the slow uptake of object-oriented programming in secondary school and presents an approach to change the style of teaching Programming. The approach is illustrated through a suggested solution of an entrance exam task in Informatics at the University of Plovdiv using C#.<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Hristo Krushkov, Assoc. Prof.<\/p>\n<p>University&nbsp;of&nbsp;Plovdiv<\/p>\n<hr \/>\n<p><strong><a name=\"art07\"><\/a> \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0418\u0422\u0415 \u0418\u0413\u0420\u0418 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u041f\u0420\u0415\u0414\u0418\u0417\u0412\u0418\u041a\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u0410 \u0418 \u0412\u042a\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0418<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041c\u0430\u044f \u0421\u0442\u043e\u044f\u043d\u043e\u0432\u0430, \u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430, \u041a\u043e\u0441\u0442\u0430\u0434\u0438\u043d \u0421\u0430\u043c\u0430\u0440\u0434\u0436\u0438\u0435\u0432<\/strong><\/p>\n<p>\u042e\u0433\u043e\u0437\u0430\u043f\u0430\u0434\u0435\u043d \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u041d. \u0420\u0438\u043b\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0438\u0433\u0440\u043e\u0432\u0438\u044f\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u0443\u0447\u0435\u0431\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441, \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d \u0432 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0441\u0440\u0435\u0434\u0430. \u041f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0441\u0435 \u043e\u043f\u0438\u0441\u0432\u0430 Kahoot! &ndash; \u0431\u0435\u0437\u043f\u043b\u0430\u0442\u043d\u0430, \u0443\u0435\u0431 \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0430 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430 \u0437\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u0438 \u0441\u043f\u043e\u0434\u0435\u043b\u044f\u043d\u0435 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u0442\u0435\u0441\u0442\u043e\u0432\u0435(\u0432\u0438\u043a\u0442\u043e\u0440\u0438\u043d\u0438) \u0432\u044a\u0432 \u0444\u043e\u0440\u043c\u0430 \u043d\u0430 \u0438\u0433\u0440\u0430, \u043a\u043e\u044f\u0442\u043e \u0434\u0430\u0432\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0434\u0430 \u0441\u0435 \u0438\u0433\u0440\u0430\u0435 \u0432 \u0440\u0435\u0430\u043b\u043d\u043e \u0432\u0440\u0435\u043c\u0435 \u043e\u0442 \u0432\u0441\u0438\u0447\u043a\u0438 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0441\u0432\u0435\u0442\u0430, \u043e\u0442 \u0432\u0441\u044f\u043a\u043e \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u043e \u0441 \u0443\u0435\u0431 \u0431\u0440\u0430\u0443\u0437\u044a\u0440 \u0438 \u0438\u043d\u0442\u0435\u0440\u043d\u0435\u0442 \u0432\u0440\u044a\u0437\u043a\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u0435 \u043f\u0440\u0438\u043c\u0435\u0440 \u0437\u0430 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 Kahoot! \u0432 \u0447\u0430\u0441 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u0438 \u0441\u0430 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0438 \u0434\u0430\u043d\u043d\u0438, \u0447\u0430\u0441\u0442 \u043e\u0442 \u0430\u043d\u043a\u0435\u0442\u0430, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0430 \u0441 \u0443\u0447\u0435\u043d\u0438\u0446\u0438, \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0449\u0438 \u0438\u0433\u0440\u043e\u0432\u0438\u044f \u0438 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u0441\u0438.<\/p>\n<p>Keywords: mathematics, educational games, gaming approach, Kahoot!<\/p>\n<p>&nbsp;<\/p>\n<p>Computer Games in Mathematics Education &#8211; Challenges and Opportunities<\/p>\n<p>Abstract.&nbsp;The article examines the gaming approach in the learning process implemented in an interactive learning environment. In details Kahoot! is explained &#8211; a free, web-based platform for creating and sharing educational tests (quizzes) in the form of a game that give oportunities to play in real time from all over the world, from any device with a web browser and Internet connection. An example is proposed f applying Kahoot! in a mathematics lesson. The data of the survey conducted with students is also analyzed using gaming and traditional approaches in training.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Ms. Maya Stoyanova<\/strong><\/p>\n<p>Dr. Daniela Dureva-Tuparova, Assoc. Prof.<\/p>\n<p>Dr. Kostadin Samardzhiev, Assoc. Prof.<\/p>\n<p>South-West University &#8211; Blagoevgrad<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDUCATIONAL MATTERS\/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418 \u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0414\u0440\u043e\u0437-\u0424\u0430\u0440\u043d\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043e \u043e\u0442 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 [Generalization of Droz-Farny Theorem Defined by a Circum-conic] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov &ndash; \u0441\u0442\u0440. 351 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 &nbsp; \u0410\u043a\u0442\u0438\u0432\u043d\u043e, \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0449\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 &ndash; \u0442\u0438\u043f \u0438\u043d\u0442\u0435\u0440\u0432\u044e [In-depth Interview] \/ \u0425\u0440\u0438\u0441\u0442\u043e \u0425\u0440\u0438\u0441\u0442\u043e\u0432, \u0425\u0440\u0438\u0441\u0442\u043e [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[3290],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - 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