{"id":43196,"date":"2018-11-17T13:16:46","date_gmt":"2018-11-17T10:16:46","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-3\/6-lxi-2018\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"6-lxi-2018","status":"publish","type":"post","link":"https:\/\/mathinfo.azbuki.bg\/en\/matematics\/matharticles2016-3\/6-lxi-2018\/","title":{"rendered":"Mathematics and Informatics, Number 6\/2018, Volume 61"},"content":{"rendered":"<p><a name=\"top\"><\/a><strong>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>\u00a0<\/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\">\u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u044b Casio \u043a\u0430\u043a \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f <\/a><br \/><a href=\"#art01\">[Graphing Calculator Casio as a Means of Professionalization of Fundamental Education] \/ <\/a><br \/><em>\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d, \u0418\u0440\u0438\u043d\u0430 \u0421\u043b\u043e\u0431\u043e\u0434\u0441\u043a\u0430\u044f \/ Alexandr Lukankin, Irina Slobodskaya<\/em> \u2013 \u0441\u0442\u0440. 535<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art02\">The Role of Computer Animation in Mathematics Teaching \/ <\/a>\u00a0<br \/><em>Sergey Larin, Valeriy Mayer <\/em>\u2013 \u0441\u0442\u0440. 542<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art03\">\u0423\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u043d\u043e \u0434\u0435\u0444\u0438\u043d\u0438\u0440\u0430\u043d\u0438\u0442\u0435 \u043c\u0440\u0435\u0436\u0438 \u0441 Floodlight Controller <\/a><br \/><a href=\"#art03\">[Management of Software Defined Networks with Floodlight Controller] \/ <\/a><br \/><em>\u0420\u0443\u043c\u0435\u043d \u0422\u043e\u0434\u043e\u0440\u043e\u0432 \/ <\/em><em>Rumen Todorov<\/em> \u2013 \u0441\u0442\u0440. 553<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p class=\"Pa23\">\u201e<a href=\"#art04\">\u042d\u043d\u0446\u0438\u043a\u043b\u043e\u043f\u0435\u0434\u0438\u044f \u0437\u0430\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u0438\u0445 \u043a\u0440\u0438\u0432\u044b\u0445\u201c \u2013 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u044b\u0439 \u0441\u0435\u0442\u0435\u0432\u043e\u0439 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0439 \u043f\u0440\u043e\u0435\u043a\u0442 \u0432 \u0440\u0430\u043c\u043a\u0430\u0445 mite <\/a><br \/><a href=\"#art04\">[Ency\u0441lopedia of Notable Plane Curves an International Network Research Project Within the Frames of Mite] \/<\/a><em> <br \/>\u0420\u043e\u0437\u0430 \u0410\u0442\u0430\u043c\u0443\u0440\u0430\u0442\u043e\u0432\u0430, M\u0438\u0445\u0430\u0438\u043b A\u043b\u0444\u0451\u0440\u043e\u0432, \u041c\u0430\u0440\u0438\u043d\u0430 \u0411\u0435\u043b\u043e\u0440\u0443\u043a\u043e\u0432\u0430, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0412\u0430\u043b\u0435\u0440\u0438\u0439 \u041c\u0430\u0439\u0435\u0440, \u0413\u0435\u043d\u0430\u0434\u0438\u0439 \u041a\u043b\u0435\u043a\u043e\u0432\u043a\u0438\u043d, \u0420\u0430\u0438\u0441\u0430 \u041e\u0432\u0447\u0438\u043d\u043d\u0438\u043a\u043e\u0432\u0430, \u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430, \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u042f\u0441\u0442\u0440\u0435\u0431\u043e\u0432 \/ Roza Atamuratova, Mikhail Alferov, Marina Belorukova, Veselin Nenkov, Valery Mayer, Gennady Klekovkin, Raisa Ovchinnikova, Maria Shabanova, Alexander Yastrebov\u00a0<\/em><strong>\u2013<\/strong> \u0441\u0442\u0440. 566<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"Pa23\">\u00a0<\/p>\n<p><a href=\"#art05\">\u0418\u0434\u0435\u043d\u0442\u0438\u0444\u0438\u0446\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043d\u0430\u0434\u0430\u0440\u0435\u043d\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0447\u0440\u0435\u0437 \u0444\u0435\u043d\u043e\u043c\u0435\u043d\u0438\u0442\u0435 \u043d\u0430 \u0416\u0430\u043d \u041f\u0438\u0430\u0436\u0435 <\/a><br \/><a href=\"#art05\">[Identification of Gifted Students in Mathematics by Jean Piaget\u2019s Phenomena] \/ <\/a><br \/><em>\u041c\u0438\u043b\u0435\u043d \u0417\u0430\u043c\u0444\u0438\u0440\u043e\u0432 \/ <\/em><em>Milen Zamfirov <\/em>\u2013 \u0441\u0442\u0440. 585<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><em>\u00a0<\/em><\/p>\n<p><strong>EDUCATIONAL TECHNOLOGIES \/ \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 class=\"Pa23\"><a href=\"#art06\">A New Meaning of the Notion \u201cExpansion of a Number\u201d <\/a><br \/><a href=\"#art06\">[\u0415\u0434\u043d\u043e \u043d\u043e\u0432\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u201e\u0440\u0430\u0437\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 \u0447\u0438\u0441\u043b\u043e\u201c] \/ <\/a><br \/><em>Rosen Nikolaev, Tanka Milkova, Radan Miryanov \/ Rosen Nikolaev, Tanka Milkova, Radan Miryanov<\/em>\u2013 \u0441\u0442\u0440. 596<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"Pa23\">\u00a0<\/p>\n<p class=\"Pa23\"><a href=\"#art07\">\u0415\u0444\u0435\u043a\u0442\u044a\u0442 \u043e\u0442 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u043e \u043b\u0438\u0447\u043d\u043e\u0441\u0442\u043d\u043e \u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432\u044a\u0440\u0445\u0443 \u0443\u0441\u043f\u0435\u0445\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043f\u0440\u0438 \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0438\u043c\u043d\u0430\u0437\u0438\u0430\u043b\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0441\u0442\u0435\u043f\u0435\u043d \u0438 \u043d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0432\u044a\u043d\u0448\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 <\/a><br \/><a href=\"#art07\">[The Effect of the Application of Interactive Personality-Oriented Training in Mathematics on the Success of Pupils at Completion of Lower Gymnasia Education Degree and National External Evaluation] \/ <\/a><br \/><em>\u0414\u043e\u0431\u0440\u0438\u043d\u0430 \u0412\u0435\u043b\u0438\u043d\u043e\u0432\u0430, \u0418\u0432\u0435\u043b\u0438\u043d\u0430 \u0428\u0443\u043c\u0430\u043a\u043e\u0432\u0430\u00a0<\/em><em>\/ Dobrina Velinova, Ivelina Shumakova\u00a0<\/em>\u2013 \u0441\u0442\u0440. 603<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/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 Issue] \u2013 \u0441\u0442\u0440. 614<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/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 1, 2018 <br \/>[Solutions of the Contest Problems from issue 1, 2018] \u2013 \u0441\u0442\u0440. 616<br \/><a href=\"https:\/\/mathinfo.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p class=\"BasicParagraph\"><strong>READ IN THE LATEST ISSUES OF \u201eAZBUKI\u201c JOURNALS \/ \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 \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> \u2013 \u0441\u0442\u0440. 626<\/p>\n<p class=\"BasicParagraph\">\u00a0<\/p>\n<p class=\"Pa14\"><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> \u2013 \u0441\u0442\u0440. 628<\/p>\n<p class=\"BasicParagraph\" style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p class=\"BasicParagraph\" style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art01\"><\/a>\u0413\u0420\u0410\u0424\u0418\u0427\u0415\u0421\u041a\u0418\u0415 \u041a\u0410\u041b\u042c\u041a\u0423\u041b\u042f\u0422\u041e\u0420\u042b CASIO \u041a\u0410\u041a \u0421\u0420\u0415\u0414\u0421\u0422\u0412\u041e \u041f\u0420\u041e\u0424\u0415\u0421\u0421\u0418\u041e\u041d\u0410\u041b\u0418\u0417\u0410\u0426\u0418\u0418 \u0424\u0423\u041d\u0414\u0410\u041c\u0415\u041d\u0422\u0410\u041b\u042c\u041d\u041e\u0413\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u042f<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d, \u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u0438\u0439 \u0440\u0435\u0433\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0441\u043e\u0446\u0438\u0430\u043b\u044c\u043d\u043e-\u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u0418\u0440\u0438\u043d\u0430 \u0421\u043b\u043e\u0431\u043e\u0434\u0441\u043a\u0430\u044f, \u0412\u043e\u043b\u043e\u0433\u043e\u0434\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u043f\u0440\u0430\u0432\u0430 \u0438 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0438 \u0424\u0421\u0418\u041d \u0420\u043e\u0441\u0441\u0438\u0438<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p class=\"Pa21\"><strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0441\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0437\u0440\u0435\u043d\u0438\u044f \u043d\u0430 \u0440\u043e\u043b\u044c \u0438 \u043c\u0435\u0441\u0442\u043e \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0432 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u043c \u043e\u0431\u0449\u0435\u0441\u0442\u0432\u0435. \u041e\u0441\u043d\u043e\u0432\u043d\u043e\u0439 \u0438\u0434\u0435\u0435\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u044f \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u044b\u0445 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0440\u0435\u0441\u0443\u0440\u0441\u043e\u0432. \u0421\u0434\u0435\u043b\u0430\u043d\u044b \u0432\u044b\u0432\u043e\u0434\u044b \u043e \u0442\u043e\u043c, \u0447\u0442\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0443\u0441\u0438\u043b\u0438\u0442\u044c \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0443\u044e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f.<\/p>\n<p>Keywords: fundamental mathematical knowledge; information technology; CASIO<\/p>\n<p>\u00a0<\/p>\n<p><strong>GRAPHING CALCULATOR CASIO AS A MEANS OF PROFESSIONALIZATION OF FUNDAMENTAL EDUCATION<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Abstract. <\/strong>The article presents the authors\u2019 point of view on the role and place of fundamental mathematical knowledge in modern society. The main idea is the need to review the process of creating and using electronic educational resources. Conclusions are drawn that information technologies allow to strengthen professional orientation of fundamental education.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Alexandr Lukankin, Assoc. Prof.<\/p>\n<p>Moscow Regional Socially-Economical Institute<\/p>\n<p>Vidnoe, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Irina Slobodskaya, Assoc. Prof.<\/p>\n<p>Vologda Institute of Law and Economics<\/p>\n<p>Vologda, Russia<\/p>\n<p style=\"text-align: right;\"><strong>\u00a0<\/strong><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art02\"><\/a>THE ROLE OF COMPUTER ANIMATION IN MATHEMATICS TEACHING<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>Sergey Larin, Valeriy Mayer<\/p>\n<p>Krasnoyarsk State Pedagogical University (Russia)<\/p>\n<p>\u00a0<\/p>\n<p class=\"Pa21\"><strong>Abstract<\/strong>. The article is devoted to the role, importance, and use of animated drawings created on computer screens in GeoGebra platform for Mathematics teaching at schools and Universities. The use of this platform introduces a new kind of visibility in Mathematics learning, which entails not only an increased interest to the subject, but also promotes understanding and stronger perception of abstract material. In addition, an opportunity appears to remove computing difficulties, since the calculations are done by the computer. The user becomes a manager of computing and this saves time, but also allows acquiring new competence in useful digital technologies in education. Animated graphics help to realize experiments, to notice new patterns, to suggest solutions of mathematical problems and to illustrate them successfully. All that is of great importance for the formation of the new generation, called upon the development of the Russian digital economy.<\/p>\n<p>Keywords: entertainment figure; GeoGebra; computational problem; lima\u00e7on (Pascal\u2019s snail); quadratic polynomial in the complex plane<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sergey Larin, DSc.<\/p>\n<p>Prof. Valeriy Mayer, DSc.<\/p>\n<p>School of Mathematics, Physics and Computer Technology<\/p>\n<p>Krasnoyarsk State Pedagogical University<\/p>\n<p>Krasnoyarsk, Russia<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art03\"><\/a>\u0423\u041f\u0420\u0410\u0412\u041b\u0415\u041d\u0418\u0415 \u041d\u0410 \u0421\u041e\u0424\u0422\u0423\u0415\u0420\u041d\u041e \u0414\u0415\u0424\u0418\u041d\u0418\u0420\u0410\u041d\u0418\u0422\u0415 \u041c\u0420\u0415\u0416\u0418 \u0421 FLOODLIGHT CONTROLLER<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>\u0420\u0443\u043c\u0435\u043d \u0422\u043e\u0434\u043e\u0440\u043e\u0432<\/p>\n<p>Sofia University<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Abstract<\/strong>. \u041e\u0441\u043d\u043e\u0432\u043d\u0430\u0442\u0430 \u0438\u0434\u0435\u044f \u043f\u0440\u0438 \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u043d\u043e \u0434\u0435\u0444\u0438\u043d\u0438\u0440\u0430\u043d\u0438\u0442\u0435 \u043c\u0440\u0435\u0436\u0438 SDN (Software Defined Networking) \u0435 \u0440\u0430\u0437\u0434\u0435\u043b\u044f\u043d\u0435\u0442\u043e \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438\u0442\u0435, \u043a\u043e\u0438\u0442\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u044f\u0432\u0430\u0442 \u043c\u0440\u0435\u0436\u0430\u0442\u0430 (control plane), \u043e\u0442 \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u0430\u0442\u0430, \u043a\u043e\u0438\u0442\u043e \u043f\u0440\u0435\u0434\u0430\u0432\u0430\u0442 \u0434\u0430\u043d\u043d\u0438\u0442\u0435 (data plane). \u041f\u043e \u0442\u043e\u0437\u0438 \u043d\u0430\u0447\u0438\u043d \u0441\u0435 \u0434\u0435\u0444\u0438\u043d\u0438\u0440\u0430 \u0441\u043b\u043e\u0439 \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043a\u043e\u043d\u0442\u0440\u043e\u043b \u043d\u0430 \u0446\u044f\u043b\u0430\u0442\u0430 \u043c\u0440\u0435\u0436\u0430 (control layer). SDN \u043a\u043e\u043d\u0442\u0440\u043e\u043b\u0435\u0440\u044a\u0442 \u0443\u043f\u0440\u0430\u0432\u043b\u044f\u0432\u0430 \u0446\u044f\u043b\u0430\u0442\u0430 \u043c\u0440\u0435\u0436\u0430, \u043f\u043e\u043b\u0443\u0447\u0430\u0432\u0430 \u0443\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0438 \u0438\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u043e\u0442 \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0438\u044f (application layer) \u0441\u043b\u043e\u0439 \u0438 \u0433\u0438 \u043f\u0440\u0435\u043f\u0440\u0435\u0434\u0430\u0432\u0430 \u043a\u044a\u043c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0438\u0442\u0435 \u043d\u0430 \u043c\u0440\u0435\u0436\u0430\u0442\u0430. \u041a\u043e\u043d\u0442\u0440\u043e\u043b\u0435\u0440\u044a\u0442 \u0438\u0437\u0432\u043b\u0438\u0447\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u0437\u0430 \u043c\u0440\u0435\u0436\u0430\u0442\u0430 \u043e\u0442 \u043c\u0440\u0435\u0436\u043e\u0432\u0438 \u0443\u0441\u0442\u0440\u043e\u0439\u0441\u0442\u0432\u0430 \u2013 \u0438\u043d\u0444\u0440\u0430\u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0435\u043d \u0441\u043b\u043e\u0439 (infrastructure layer) \u2013 \u0438 \u044f \u0432\u0440\u044a\u0449\u0430 \u043e\u0431\u0440\u0430\u0442\u043d\u043e \u043a\u044a\u043c \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0438\u044f \u0441\u043b\u043e\u0439. \u0412 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u0449\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043e\u0441\u043d\u043e\u0432\u043d\u0430\u0442\u0430 \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438\u0442\u0435 \u043d\u0430 Floodlight \u043a\u043e\u043d\u0442\u0440\u043e\u043b\u0435\u0440\u0430. \u0422\u0435\u0441\u0442\u0432\u0430\u043c\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u0442\u043e\u043f\u043e\u043b\u043e\u0433\u0438\u0438 \u043d\u0430 \u043c\u0440\u0435\u0436\u043e\u0432\u0438\u044f \u0441\u0438\u043c\u0443\u043b\u0430\u0442\u043e\u0440 Mininet, \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0438 \u043c\u0430\u0448\u0438\u043d\u0438, \u0434\u043e\u0431\u0430\u0432\u044f\u043d\u0435 \u0438 \u043f\u0440\u0438\u0445\u0432\u0430\u0449\u0430\u043d\u0435 \u043d\u0430 OpenFlow \u043f\u043e\u0442\u043e\u0446\u0438 \u043e\u0442 \u043c\u0440\u0435\u0436\u043e\u0432\u0438\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430\u0442\u043e\u0440 Wireshark.<\/p>\n<p>Keywords:Software Defined Networking; Floodlight Controller; OpenFlow<\/p>\n<p>\u00a0<\/p>\n<p><strong>MANAGEMENT OF SOFTWARE DEFINED NETWORKS WITH FLOODLIGHT CONTROLLER<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Abstract. <\/strong>The basic idea for software-defined networks (SDN) is the separation of systems that control the network from systems the data plane. This defines a layer of program control and control of the whole network (control layer). The SDN controller manages the entire network, receives instructions and instructions from the application layer and relays them to the network components. The controller retrieves network infrastructure information \u2013 a infrastructure layer \u2013 and returns it back to the application layer. In this article we will present the basic architecture and features of the Floodlight controller. We test different topologies of the Mininet network simulator, interaction between virtual machines, adding and intercepting OpenFlow flows from the Wireshark network analyzer.<\/p>\n<p>\u00a0<\/p>\n<p>Mr. Rumen Todorov, PhD student<\/p>\n<p>University of Sofia<\/p>\n<p>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art04\"><\/a>\u201e\u042d\u041d\u0426\u0418\u041a\u041b\u041e\u041f\u0415\u0414\u0418\u042f \u0417\u0410\u041c\u0415\u0427\u0410\u0422\u0415\u041b\u042c\u041d\u042b\u0425 \u041f\u041b\u041e\u0421\u041a\u0418\u0425 \u041a\u0420\u0418\u0412\u042b\u0425\u201c \u2013 \u041c\u0415\u0416\u0414\u0423\u041d\u0410\u0420\u041e\u0414\u041d\u042b\u0419 \u0421\u0415\u0422\u0415\u0412\u041e\u0419 \u0418\u0421\u0421\u041b\u0415\u0414\u041e\u0412\u0410\u0422\u0415\u041b\u042c\u0421\u041a\u0418\u0419 \u041f\u0420\u041e\u0415\u041a\u0422 \u0412 \u0420\u0410\u041c\u041a\u0410\u0425 MITE<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>\u0420\u043e\u0437\u0430 \u0410\u0442\u0430\u043c\u0443\u0440\u0430\u0442\u043e\u0432\u0430, \u041e\u0431\u043b\u0430\u0441\u0442\u043d\u0430\u044f \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u0430\u044f \u0448\u043a\u043e\u043b\u0430-\u0438\u043d\u0442\u0435\u0440\u043d\u0430\u0442 \u0434\u043b\u044f \u043e\u0434\u0430\u0440\u0435\u043d\u043d\u044b\u0445 \u0434\u0435\u0442\u0435\u0439 \u0441 \u0443\u0433\u043b\u0443\u0431\u043b\u0435\u043d\u043d\u044b\u043c \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435\u043c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u043c\u0435\u0442\u043e\u0432 \u2013 \u0410\u043a\u0442\u0430\u0443 (\u041a\u0430\u0437\u0430\u0445\u0441\u0442\u0430\u043d)<\/p>\n<p>M\u0438\u0445\u0430\u0438\u043b A\u043b\u0444\u0451\u0440\u043e\u0432, \u0410\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u0441\u043e\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u2013 \u041c\u043e\u0441\u043a\u0432\u0430 (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u041c\u0430\u0440\u0438\u043d\u0430 \u0411\u0435\u043b\u043e\u0440\u0443\u043a\u043e\u0432\u0430, \u0421\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430 \u2116 8 \u2013 \u0410\u0440\u0445\u0430\u043d\u0433\u0435\u043b\u044c\u0441\u043a (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0412\u044b\u0441\u0448\u0430\u044f \u0432\u043e\u0435\u043d\u043d\u043e\u043c\u043e\u0440\u0441\u043a\u0430\u044f \u0448\u043a\u043e\u043b\u0430 \u201e\u041d. \u0419. \u0412\u0430\u043f\u0446\u0430\u0440\u043e\u0432\u201c (\u0411\u043e\u043b\u0433\u0430\u0440\u0438\u044f)<\/p>\n<p>\u0412\u0430\u043b\u0435\u0440\u0438\u0439 \u041c\u0430\u0439\u0435\u0440, \u041a\u0440\u0430\u0441\u043d\u043e\u044f\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u2013 \u041a\u0440\u0430\u0441\u043d\u043e\u044f\u0440\u0441\u043a (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u0413\u0435\u043d\u0430\u0434\u0438\u0439 \u041a\u043b\u0435\u043a\u043e\u0432\u043a\u0438\u043d, \u0421\u0430\u043c\u0430\u0440\u0441\u043a\u0438\u0439 \u0444\u0438\u043b\u0438\u0430\u043b \u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u0420\u0430\u0438\u0441\u0430 \u041e\u0432\u0447\u0438\u043d\u043d\u0438\u043a\u043e\u0432\u0430, \u0421\u0435\u0432\u0435\u0440\u043d\u044b\u0439 (\u0410\u0440\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439) \u0444\u0435\u0434\u0435\u0440\u0430\u043b\u044c\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u2013 \u0410\u0440\u0445\u0430\u043d\u0433\u0435\u043b\u044c\u0441\u043a (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430, \u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u0438\u0439 \u0446\u0435\u043d\u0442\u0440 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u043a\u0430\u0434\u0440\u043e\u0432\u043e\u0433\u043e \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u2013 \u041c\u043e\u0441\u043a\u0432\u0430 (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u042f\u0441\u0442\u0440\u0435\u0431\u043e\u0432, \u042f\u0440\u043e\u0441\u043b\u0430\u0432\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u2013 \u042f\u0440\u043e\u0441\u043b\u0430\u0432\u043b\u044c (\u0420\u043e\u0441\u0441\u0438\u044f)<\/p>\n<p>\u00a0<\/p>\n<p class=\"Pa21\"><strong>\u0410\u043d\u043d\u043e\u0442\u0430\u0446\u0438\u044f<em>. <\/em><\/strong>\u041e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0437\u0430\u0434\u0430\u0447 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0435\u043a\u0442\u0430 \u201e\u041c\u0435\u0442\u043e\u0434\u0438\u043a\u0438 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438 (MITE)\u201c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0439, \u043f\u043e\u0431\u0443\u0436\u0434\u0430\u044e\u0449\u0438\u0445 \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f, \u0443\u0447\u0438\u0442\u0435\u043b\u0435\u0439 \u0438 \u0443\u0447\u0435\u043d\u044b\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u0441\u0442\u0440\u0430\u043d \u043a \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044e \u0432 \u043d\u0430\u0443\u0447\u043d\u044b\u0445 \u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0446\u0435\u043b\u044f\u0445. \u0418\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u043e\u0439 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0442\u0430\u043a\u043e\u0433\u043e \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0435\u0442\u0435\u0432\u044b\u0435 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0435 \u043f\u0440\u043e\u0435\u043a\u0442\u044b. \u041f\u0440\u043e\u0435\u043a\u0442, \u043d\u0430\u0447\u0430\u0442\u044b\u0439 \u0432 2018 \u0433., \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d \u043d\u0430 \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435 \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u0439 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0439 \u044d\u043d\u0446\u0438\u043a\u043b\u043e\u043f\u0435\u0434\u0438\u0438 \u043f\u043b\u043e\u0441\u043a\u0438\u0445 \u043a\u0440\u0438\u0432\u044b\u0445. \u0414\u043b\u044f \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0430 \u0431\u044b\u043b \u0441\u043e\u0437\u0434\u0430\u043d \u0441\u0430\u0439\u0442 \u201e\u041f\u0438\u0448\u0435\u043c \u0441\u0430\u043c\u0438\u201d, \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0443\u0447\u0435\u043d\u044b\u0435 \u2013 \u043c\u043e\u0434\u0435\u0440\u0430\u0442\u043e\u0440\u044b \u0440\u0430\u0437\u0434\u0435\u043b\u043e\u0432 \u044d\u043d\u0446\u0438\u043a\u043b\u043e\u043f\u0435\u0434\u0438\u0438 \u2013 \u0432\u044b\u043b\u043e\u0436\u0438\u043b\u0438 \u0437\u0430\u0434\u0430\u043d\u0438\u044f \u0434\u043b\u044f \u0438\u0441\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u0435\u0439 \u0432 \u0444\u043e\u0440\u043c\u0435 \u0441\u0442\u0430\u0442\u0435\u0439-\u043c\u0430\u0442\u0440\u0438\u0446. \u0418\u0441\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044f\u043c\u0438 \u044f\u0432\u043b\u044f\u043b\u0438\u0441\u044c \u043a\u043e\u043c\u0430\u043d\u0434\u044b \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0442\u0440\u0435\u0445 \u0441\u0442\u0440\u0430\u043d \u2013 \u0411\u043e\u043b\u0433\u0430\u0440\u0438\u0438, \u041a\u0430\u0437\u0430\u0445\u0441\u0442\u0430\u043d\u0430 \u0438 \u0420\u043e\u0441\u0441\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0430\u0431\u043e\u0442\u0430\u043b\u0438 \u043f\u043e\u0434 \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e\u043c \u0441\u0432\u043e\u0438\u0445 \u043d\u0430\u0441\u0442\u0430\u0432\u043d\u0438\u043a\u043e\u0432. \u0414\u0430\u043d\u043d\u0430\u044f \u0441\u0442\u0430\u0442\u044c\u044f \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0440\u0430\u0431\u043e\u0442\u0443 \u0432\u0441\u0435\u0445 \u0442\u0435\u0445, \u043a\u0442\u043e \u043f\u043e\u043c\u043e\u0433\u0430\u043b \u0443\u0447\u0430\u0449\u0438\u043c\u0441\u044f \u0432 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432.<\/p>\n<p>Keywords: secondary education; network research project; crowd sourcing project; cloud services; dynamic mathematics system; experimental mathematics<\/p>\n<p>\u00a0<\/p>\n<p><strong>ENCY\u0421LOPEDIA OF NOTABLE PLANE CURVES AN INTERNATIONAL NETWORK RESEARCH PROJECT WITHIN THE FRAMES OF MITE<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract. <\/strong>Creation of conditions to motivate students, teachers and scientists from different countries by including them in a network is one of the goals of the International project \u201cMethods and Information technologies in educations\u201d (MITE). Crowd sourcing for a research project is an interesting form for the purpose. The project began in 2018 and was directed to the elaboration of an open electronic encyclopedia of plane curves. A website \u201cWe write by ourselves\u201d was created to support the project. Scientists were the moderators of the encyclopedia topics. They formulated problems in articles-matrices. The participants in the project tried to solve the problems and wrote articles too. They were grouped in teams consisted of students from three countries \u2013 Bulgaria, Kazakhstan and Russia. Their mentors were school teachers. The present article describes the technical and methodological work of those who helped students to obtain results.<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Roza Atamuratova, teacher<\/p>\n<p>Regional Special Boarding School for Gifted Children with Profound Studying of Different Subjects<\/p>\n<p>Aktau, Kazakhstan<\/p>\n<p>\u00a0<\/p>\n<p>Mr. Mikhail Alferov<\/p>\n<p>Academy of Public Administration<\/p>\n<p>Moscow, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Marina Belorukova, teacher<\/p>\n<p>Public Secondary School \u2116 8<\/p>\n<p>Arkhangelsk, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<\/p>\n<p>\u201cNikola Vaptsarov\u201d Naval Academy<\/p>\n<p>Varna, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Valery Mayer, DSc.<\/p>\n<p>V. P. Astafev Krasnoyarsk State Pedagogical University<\/p>\n<p>Krasnoyarsk , Russia<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Gennady Klekovkin, Assoc. Prof.<\/p>\n<p>Moscow State Pedagogical University \u2013 Samara Branch<\/p>\n<p>Samara, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Raisa Ovchinnikova, Assoc. Prof.<\/p>\n<p>M.V. Lomonosov Northern (Arctic) Federal University<\/p>\n<p>Arkhangelsk, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Maria Shabanova, DSc.<\/p>\n<p>Moscow Center for Human Resource Development<\/p>\n<p>Moscow, Russia<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Alexander Yastrebov, DSc.<\/p>\n<p>K. D. Ushinski Yaroslavl State Pedagogical University<\/p>\n<p>Yaroslavl, Russia<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art05\"><\/a>\u0418\u0414\u0415\u041d\u0422\u0418\u0424\u0418\u0426\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u041d\u0410\u0414\u0410\u0420\u0415\u041d\u0418 \u0423\u0427\u0415\u041d\u0418\u0426\u0418 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0427\u0420\u0415\u0417 \u0424\u0415\u041d\u041e\u041c\u0415\u041d\u0418\u0422\u0415 \u041d\u0410 \u0416\u0410\u041d \u041f\u0418\u0410\u0416\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Milen Zamfirov<\/p>\n<p>Sofia University<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043e\u043f\u0438\u0441\u0432\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0442\u0430 \u0437\u0430 \u0438\u0434\u0435\u043d\u0442\u0438\u0444\u0438\u0446\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043d\u0430\u0434\u0430\u0440\u0435\u043d\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0430 \u043d\u0430 \u0444\u0435\u043d\u043e\u043c\u0435\u043d\u0438\u0442\u0435 \u043d\u0430 \u0416. \u041f\u0438\u0430\u0436\u0435. \u041f\u043e\u043a\u0430\u0437\u0432\u0430 \u0441\u0435, \u0447\u0435 \u0447\u0440\u0435\u0437 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0444\u0435\u043d\u043e\u043c\u0435\u043d\u0438\u0442\u0435, \u043e\u0441\u043e\u0431\u0435\u043d\u043e \u0442\u0435\u0437\u0438, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043f\u043e\u0437\u043d\u0430\u043d\u0438\u0435, \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438 \u0443\u043c\u0441\u0442\u0432\u0435\u043d\u0430\u0442\u0430 \u0432\u044a\u0437\u0440\u0430\u0441\u0442 \u043d\u0430 \u0434\u0430\u0434\u0435\u043d \u0443\u0447\u0435\u043d\u0438\u043a, \u043e\u0442\u0442\u0430\u043c \u0438 \u0434\u0430 \u0441\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438 \u043a\u0430\u043a\u0432\u043e \u0435 \u0438\u043d\u0442\u0435\u043b\u0435\u043a\u0442\u0443\u0430\u043b\u043d\u043e\u0442\u043e \u043c\u0443 \u043d\u0438\u0432\u043e.<\/p>\n<p>Keywords: Piaget\u2018s theory; development process; mathematics; gifted student<\/p>\n<p>\u00a0<\/p>\n<p><strong>IDENTIFICATION OF GIFTED STUDENTS IN MATHEMATICS BY JEAN PIAGET\u2019S PHENOMENA<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract. <\/strong>This paper describes the possibility of identification of gifted in Mathematics students based on Jean Piaget\u2019s phenomena. It shows that by conducting some of his phenomena \u2013 the ones related to mathematical knowledge in particular \u2013 it allows to calculate the mental age of a student and after that their intellectual level to be determined.<\/p>\n<p>\u00a0<\/p>\n<p>Assoc. Prof. Milen Zamfirov, DSc.<\/p>\n<p>Department of Special Education and Speech Therapy<\/p>\n<p>Sofia University<\/p>\n<p>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art06\"><\/a>A NEW MEANING OF THE NOTION \u201cEXPANSION OF A NUMBER\u201d<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>Rosen Nikolaev, Tanka Milkova, Radan Miryanov<\/p>\n<p>University of Economics \u2013 Varna (Bulgaria)<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract. <\/strong>In the present paper a new meaning of the notion \u201cexpansion of a number\u201d is proposed by the authors. Some interesting problems are considered with corresponding answers and summarized results. The idea is by means of only one digit (used several times) and different mathematical symbols, signs and operations, to express (to expand) other digits. The research could be used by students and teachers to generate new examples with educational purposes or to find alternative variants of the problems in the paper.<\/p>\n<p>Keywords: digit; mathematical sign; operation; expansion<\/p>\n<p>\u00a0<\/p>\n<p><strong>\u0415\u0414\u041d\u041e \u041d\u041e\u0412\u041e \u0417\u041d\u0410\u0427\u0415\u041d\u0418\u0415 \u041d\u0410 \u041f\u041e\u041d\u042f\u0422\u0418\u0415\u0422\u041e \u201e\u0420\u0410\u0417\u041b\u0410\u0413\u0410\u041d\u0415 \u041d\u0410 \u0427\u0418\u0421\u041b\u041e\u201c<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Abstract. <\/strong>\u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442 \u0435\u0434\u043d\u043e \u043d\u043e\u0432\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u201e\u0440\u0430\u0437\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 \u0447\u0438\u0441\u043b\u043e\u201c. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441\u044a\u0441 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438 \u043e\u0442\u0433\u043e\u0432\u043e\u0440\u0438 \u0438 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438. \u0418\u0434\u0435\u044f\u0442\u0430 \u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0441\u0430\u043c\u043e \u0435\u0434\u043d\u0430 \u0446\u0438\u0444\u0440\u0430 (\u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0430 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u043f\u044a\u0442\u0438) \u0438 \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0438\u043c\u0432\u043e\u043b\u0438, \u0437\u043d\u0430\u0446\u0438 \u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0434\u0430 \u0441\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u0442 (\u0440\u0430\u0437\u043b\u043e\u0436\u0430\u0442) \u0434\u0440\u0443\u0433\u0438 \u0446\u0438\u0444\u0440\u0438. \u0418\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435\u0442\u043e \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u043e\u0442 \u0443\u0447\u0438\u0442\u0435\u043b\u0438 \u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0437\u0430 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043d\u043e\u0432\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0441 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u0446\u0435\u043b\u0438 \u0438\u043b\u0438 \u0434\u0430 \u0441\u0435 \u043d\u0430\u043c\u0435\u0440\u044f\u0442 \u0430\u043b\u0442\u0435\u0440\u043d\u0430\u0442\u0438\u0432\u043d\u0438 \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Dr. Rosen Nikolaev<\/p>\n<p>Dr. Tanka Milkova, Assoc. Prof.<\/p>\n<p>Dr. Radan Miryanov, Assoc. Prof.<\/p>\n<p>University of Economics \u2013 Varna<\/p>\n<p>Varna, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong><a name=\"art07\"><\/a>\u0415\u0424\u0415\u041a\u0422\u042a\u0422 \u041e\u0422 \u041f\u0420\u0418\u041b\u0410\u0413\u0410\u041d\u0415\u0422\u041e \u041d\u0410 \u0418\u041d\u0422\u0415\u0420\u0410\u041a\u0422\u0418\u0412\u041d\u041e \u041b\u0418\u0427\u041d\u041e\u0421\u0422\u041d\u041e \u041e\u0420\u0418\u0415\u041d\u0422\u0418\u0420\u0410\u041d\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0412\u042a\u0420\u0425\u0423 \u0423\u0421\u041f\u0415\u0425\u0410 \u041d\u0410 \u0423\u0427\u0415\u041d\u0418\u0426\u0418\u0422\u0415 \u041f\u0420\u0418 \u0417\u0410\u0412\u042a\u0420\u0428\u0412\u0410\u041d\u0415 \u041d\u0410 \u041f\u0420\u041e\u0413\u0418\u041c\u041d\u0410\u0417\u0418\u0410\u041b\u041d\u0410 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0410 \u0421\u0422\u0415\u041f\u0415\u041d \u0418 \u041d\u0410\u0426\u0418\u041e\u041d\u0410\u041b\u041d\u041e \u0412\u042a\u041d\u0428\u041d\u041e \u041e\u0426\u0415\u041d\u042f\u0412\u0410\u041d\u0415<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>\u0414\u043e\u0431\u0440\u0438\u043d\u0430 \u0412\u0435\u043b\u0438\u043d\u043e\u0432\u0430, \u0418\u0432\u0435\u043b\u0438\u043d\u0430 \u0428\u0443\u043c\u0430\u043a\u043e\u0432\u0430<\/p>\n<p>\u041e\u0423 \u201e\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438\u201c \u2013 \u0425\u0430\u0441\u043a\u043e\u0432\u043e<\/p>\n<p>\u00a0<\/p>\n<p class=\"Pa21\"><strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0435\u0444\u0435\u043a\u0442\u044a\u0442 \u043e\u0442 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043b\u0438\u0447\u043d\u043e\u0441\u0442\u043d\u043e \u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 (\u041b\u041e\u041e) \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432\u044a\u0440\u0445\u0443 \u043f\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435. \u0421\u0440\u0430\u0432\u043d\u0435\u043d \u0435 \u0443\u0441\u043f\u0435\u0445\u044a\u0442 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043d\u0430 \u0438\u0437\u0445\u043e\u0434\u0430 \u043d\u0430 \u041f\u041e\u0421 \u2013 VII \u043a\u043b\u0430\u0441, \u0438 \u043d\u0430 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0432\u044a\u043d\u0448\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 (\u041d\u0412\u041e). \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u043e\u0442 \u041d\u0412\u041e, \u0441\u0430 \u043c\u0430\u043b\u043a\u043e \u043f\u043e-\u043d\u0438\u0441\u043a\u0438 \u0432 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u043e\u0446\u0435\u043d\u043a\u0438\u0442\u0435 \u043f\u0440\u0438 \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e, \u043d\u043e \u0440\u0430\u0437\u043b\u0438\u043a\u0438\u0442\u0435 \u043d\u0435 \u0441\u0430 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0438. \u0420\u0430\u0437\u043b\u0438\u043a\u0438\u0442\u0435 \u0432 \u0443\u0441\u043f\u0435\u0445\u0430 \u043c\u0435\u0436\u0434\u0443 \u043c\u043e\u043c\u0438\u0447\u0435\u0442\u0430\u0442\u0430 \u0438 \u043c\u043e\u043c\u0447\u0435\u0442\u0430\u0442\u0430 \u0438 \u043c\u0435\u0436\u0434\u0443 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043e\u0442 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438 \u0438 \u0442\u0443\u0440\u0441\u043a\u0438 \u0435\u0442\u043d\u043e\u0441 \u0441\u0430 \u043c\u0430\u043b\u043a\u0438 \u0438 \u043d\u0435\u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0438. \u041c\u0435\u0436\u0434\u0443 \u0443\u0441\u043f\u0435\u0445\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u043a\u0440\u0430\u044f \u043d\u0430 VII \u043a\u043b\u0430\u0441 \u0438 \u0443\u0441\u043f\u0435\u0445\u0430 \u043d\u0430 \u041d\u0412\u041e \u0438\u043c\u0430 \u0432\u0438\u0441\u043e\u043a\u0430 \u043a\u043e\u0440\u0435\u043b\u0430\u0442\u0438\u0432\u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442 \u2013 (r = 0,825***). \u041d\u0430\u0439-\u0441\u0438\u043b\u043d\u043e \u0432\u043b\u0438\u044f\u043d\u0438\u0435 \u0432\u044a\u0440\u0445\u0443 \u0443\u0441\u043f\u0435\u0445\u0430 \u043e\u043a\u0430\u0437\u0432\u0430 \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u0443\u0447\u0435\u0431\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441 (92,526 % \u043f\u0440\u0438 \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435 \u0438 89,193 % \u043e\u0442 \u041d\u0412\u041e). \u041f\u0440\u0438 \u041d\u0412\u041e \u0431\u0440\u043e\u044f\u0442 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0441 \u0432\u0438\u0441\u043e\u043a \u0443\u0441\u043f\u0435\u0445 \u043f\u0440\u0438 \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435\u0442\u043e \u0435 \u043d\u0430\u043c\u0430\u043b\u044f\u043b \u0441 23,40 %, \u0434\u043e\u043a\u0430\u0442\u043e \u0431\u0440\u043e\u044f\u0442 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0441 \u043d\u0438\u0441\u044a\u043a \u0443\u0441\u043f\u0435\u0445 \u0441\u0435 \u0435 \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u043b \u0441 52,38 %. \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u043e\u0442 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e\u0442\u043e \u041d\u0412\u041e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043f\u043e\u043a\u0430\u0437\u0432\u0430\u0442 \u043f\u043e-\u0441\u0438\u043b\u043d\u043e \u0430\u043a\u0442\u0438\u0432\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0441 \u043f\u043e-\u043d\u0438\u0441\u044a\u043a \u0443\u0441\u043f\u0435\u0445 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043f\u043e-\u0432\u0438\u0441\u043e\u043a\u0438 \u043e\u0446\u0435\u043d\u043a\u0438 \u0432 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u0442\u0435\u0437\u0438 \u0441 \u043f\u043e-\u0432\u0438\u0441\u043e\u043a \u0443\u0441\u043f\u0435\u0445.<\/p>\n<p><em>Keywords:<\/em> mathematics; success; national external evaluation; factors; correlation<\/p>\n<p>\u00a0<\/p>\n<p><strong>THE EFFECT OF THE APPLICATION OF INTERACTIVE PERSONALITY-ORIENTED TRAINING IN MATHEMATICS ON THE SUCCESS OF PUPILS AT COMPLETION OF LOWER GYMNASIA EDUCATION DEGREE AND NATIONAL EXTERNAL EVALUATION<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract. <\/strong>The article discusses the effect of the use of personal-oriented learning (POL) in mathematics education on pupils achievements. Compared to the success of the pupils at the outcome of the Lower Gymnasium Degree (LGD) \u2013 7th grade and National External Evaluation (NEE). The results obtained from NEE are slightly lower compared to the grades when completing the training, but the differences are not statistically proven. The differences in the success of girls with boys and between pupils from Bulgarian and Turkish ethnicities are small and unproven. Between the success of the pupils at the end of the 7th grade and the success of NEE has a high correlation dependence \u2013 (r = 0,825***). The strongest influence on the success has the activity of pupil participation in the learning process (92.526% at completion and 89.193% of NEE). On NEE, the number of pupils with high success decreased by 23.40%, while the number of low-grade pupils increased by 52.38%. The results obtained from the conducted NEE in mathematics show a stronger activation of the pupils with lower success and the receipt of higher grades compared to those with higher success.<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Dobrina Velinova, Ms. Ivelina Shumakova<\/p>\n<p>\u201cSt. Kliment Ohridski\u201d Primary School<\/p>\n<p>Haskovo, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 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 \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u044b Casio \u043a\u0430\u043a \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [Graphing Calculator Casio as a Means of Professionalization of Fundamental Education] \/ \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d, \u0418\u0440\u0438\u043d\u0430 \u0421\u043b\u043e\u0431\u043e\u0434\u0441\u043a\u0430\u044f \/ Alexandr Lukankin, Irina Slobodskaya \u2013 \u0441\u0442\u0440. 535 \u00a0 The Role of Computer Animation in Mathematics Teaching \/ \u00a0Sergey Larin, Valeriy Mayer [&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":[3614],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - 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