{"id":38069,"date":"2012-06-20T18:45:55","date_gmt":"2012-06-20T15:45:55","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/math3\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"math3-2","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles\/math3-2\/","title":{"rendered":"Mathematics and Informatics, Number 3\/2012, Volume 55"},"content":{"rendered":"<p class=\"style9\" align=\"left\"><strong>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS<\/strong><\/p>\n<p class=\"style9\" align=\"left\">\n<p> <strong>\u0421\u042a\u0411\u0418\u0422\u0418\u042f \/ EVENTS<\/strong><br \/> \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0435\u043d \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u043b\u0430\u0434\u0438 \u0442\u0430\u043b\u0430\u043d\u0442\u0438\u201d 2012 <br \/>[National Competition \u201cYoung&nbsp;Talents\u201d 2012] \/ <br \/>\u0413. \u0414\u044f\u043d\u043a\u043e\u0432 \/ G. Dyankov \u2013 p. 199<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c01\"><br \/>\u0421\u0443\u0431\u0435\u043a\u0442\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u043a \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f <br \/>[Subjectivity as a Methodological Principle in Informatization of Education] \/ <\/a><br \/><em>\u0422. \u0421\u0435\u0440\u0433\u0435\u0435\u0432\u0430 \/ T. Sergeeva, \u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev<\/em> \u2013 p. 201<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c02\"><br \/>\u0414\u0438\u0441\u0442\u0430\u043d\u0446\u0438\u043e\u043d\u043d\u043e\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u0438\u043d\u043d\u043e\u0432\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f&nbsp;<br \/>[Distance Learning as Innovation Trend of Education] \/&nbsp;<br \/><\/a><em style=\"text-align: left;\">\u041b. \u0425\u0430\u0439\u043c\u0438\u043d\u0430 \/ L. Khaymina, \u0415. \u0425\u0430\u0439\u043c\u0438\u043d \/ E. Khaymin<\/em> \u2013 p. 208<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c03\"><br \/> \u0422\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0437\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u0438 \u0440\u0430\u0437\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0438\u0435\u043d\u0438\u0435 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u0443\u0447\u0435\u0431\u043d\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 <br \/>\u0438 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u0438 \u043f\u043e\u0434\u0434\u044a\u0440\u0436\u0430\u043d\u0435 \u043d\u0430 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u0437\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 <br \/>[Technological Tools for Development, Delivering and Maintenance of e-Learning Content and Courses] \/ <\/a><br \/><em>\u0413. \u0422\u0443\u043f\u0430\u0440\u043e\u0432 \/ G. Tuparov, \u0414. \u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430 \/ D. Tuparova<\/em> \u2013 p. 213<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c04\"><\/p>\n<p>\u0421\u043b\u0443\u0447\u0430\u0439\u043d\u043e \u0441\u044a\u0440\u0444\u0438\u0440\u0430\u043d\u0435 \u0432 \u0438\u043d\u0442\u0435\u0440\u043d\u0435\u0442&nbsp;<br \/><\/a><a href=\"#c04\">[Random Internet Surfing] \/&nbsp;<br \/><\/a><em style=\"text-align: left;\">\u0415. \u0421\u0442\u043e\u0438\u043c\u0435\u043d\u043e\u0432\u0430 \/ E. Stoimenova<\/em> \u2013 p. 225<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c05\"><br \/>\u0418\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0442\u0440\u0435\u0430\u043a\u0442\u043e\u0440\u0438\u044f \u2013 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u0447\u0430\u0441\u0442\u0435\u043d \u0441\u043b\u0443\u0447\u0430\u0439&nbsp;<br \/>[Individual Educational Trajectory \u2013 a Case Study] \/<br \/><\/a><em style=\"text-align: left;\">\u0411. \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ B. Lazarov <\/em>\u2013 p. 238<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><a href=\"#c06\">\u0422\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0443\u043b\u0442\u0438\u043c\u0435\u0434\u0438\u0439\u043d\u0438 \u043f\u0440\u0435\u0437\u0435\u043d\u0442\u0430\u0446\u0438\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043e\u0442 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0432 \u043e\u0441\u043c\u0438 \u043a\u043b\u0430\u0441 \u043f\u0440\u0438 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u0435\u043a\u0438\u043f<br \/>[Technological Model for Creating Multimedia Presentations in Mathematics by Students Teamwork] \/&nbsp;<\/a><br \/><em>\u041f. \u0414\u0440\u0430\u0433\u0430\u043d\u043e\u0432\u0430 \/ P. Draganova<\/em> \u2013 p. 249<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" align=\"left\"> <strong>\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \/ CONTEST PROBLEMS<\/strong><br \/><em>The column is led by Dr. Svetlozar Doychev and Dr. Veselin Nenkov<\/em><\/p>\n<p> contest problems - p. 265<\/p>\n<p>Solutions of the contest problems from issue 2, 2011 - p. 266<\/p>\n<p>Solutions of the contest problems from issue 3, 2011 - p. 271<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"> \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0443\u0440\u043d\u0438\u0440 \u201e\u0420\u0443\u043c\u0435\u043d \u0413\u0440\u043e\u0437\u0434\u0430\u043d\u043e\u0432\u201d \u043d\u0430 10 \u0433\u043e\u0434\u0438\u043d\u0438 <br \/>[Mathematical&nbsp;Tournament \u201cRumen Grozdanov\u201d &#8211; XTH Edition] \/ <br \/><em>\u0418. \u0421\u0442\u0430\u0440\u0438\u0431\u0440\u0430\u0442\u043e\u0432 \/ Y. Staribratov<\/em> \u2013 p. 274<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p class=\"style9\" style=\"text-align: left;\" align=\"left\"><strong><br \/>\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS<\/strong> \u2013 p. 284<\/p>\n<p class=\"style9\" style=\"text-align: center;\" align=\"left\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p class=\"style14\" align=\"left\"><a id=\"c01\" name=\"c01\"><\/a><strong>\u0421\u0423\u0411\u0415\u041a\u0422\u041d\u041e\u0421\u0422\u042c \u041a\u0410\u041a \u041c\u0415\u0422\u041e\u0414\u041e\u041b\u041e\u0413\u0418\u0427\u0415\u0421\u041a\u0418\u0419 \u041f\u0420\u0418\u041d\u0426\u0418\u041f&nbsp;<\/strong><strong>\u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u0417\u0410\u0426\u0418\u0418 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u042f<\/strong><\/p>\n<p><strong> \u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0421\u0435\u0440\u0433\u0435\u0435\u0432\u0430, \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432<\/strong><\/p>\n<p class=\"style9\" align=\"left\"><strong>Abstract<\/strong>. \u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u0441\u0443\u0431\u044a\u0435\u043a\u0442\u043d\u043e\u0441\u0442\u0438 \u043b\u0438\u0447\u043d\u043e\u0441\u0442\u0438 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u043e\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043b\u0435\u043d\u0438\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f, \u0440\u0430\u0441\u043a\u0440\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e-\u043a\u043e\u043c\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439 \u0432 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0435\u043d\u0438\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 \u0434\u043b\u044f \u0441\u0430\u043c\u043e\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0438 \u0441\u0430\u043c\u043e\u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043b\u0438\u0447\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p><em>Keywords<\/em>: education, informatization, subjectivity, self-education, reflection.<\/p>\n<p class=\"style9\" align=\"left\">\n<p><strong>SUBJECTIVITY AS A METHODOLOGICAL PRINCIPLE&nbsp;IN INFORMATIZATION OF EDUCATION<\/strong><\/p>\n<p class=\"style9\" align=\"left\"><strong><br \/> \u0410bstract<\/strong>. The paper considers some problems of the development of personal subjectivity in the realization process of the informatization of education. The potential of information and communication technologies is revealed in ensuring conditions for self-education and personal self-realization.<\/p>\n<p><strong>Tayana Fedorovna Sergeeva<\/strong><br \/> <em>Professor, DSc in Pedagogy<\/em><br \/><em> Head of the Department for General Mathematics<\/em><br \/><em> and Natural Science Subjects<\/em><br \/><em> Academy of Social Control<\/em><\/p>\n<p><strong>Sava Grozdev<\/strong><br \/><em>Professor, Doctor in Mathematics, DSc in Pedagogy<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p align=\"left\"><strong><a id=\"c02\" name=\"c02\"><\/a>\u0414\u0418\u0421\u0422\u0410\u041d\u0426\u0418\u041e\u041d\u041d\u041e\u0415 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u041a\u0410\u041a\u0418\u041d\u041d\u041e\u0412\u0410\u0426\u0418\u041e\u041d\u041d\u041e\u0415 \u041d\u0410\u041f\u0420\u0410\u0412\u041b\u0415\u041d\u0418\u0415 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u042f<\/p>\n<p> \u041b\u044e\u0434\u043c\u0438\u043b\u0430 \u0425\u0430\u0439\u043c\u0438\u043d\u0430, \u0415\u0432\u0433\u0435\u043d\u0438\u0439 \u0425\u0430\u0439\u043c\u0438\u043d<\/strong><\/p>\n<p align=\"left\"><strong>Abstract<\/strong>. \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0430\u0432\u0442\u043e\u0440\u0430\u043c\u0438 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0430 \u043e\u0442 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0444\u043e\u0440\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043a \u0434\u0438\u0441\u0442\u0430\u043d\u0446\u0438\u043e\u043d\u043d\u043e\u043c\u0443 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044e. \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u043e\u043f\u0440\u043e\u0441 \u043e \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0435 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u044f \u043d\u043e\u0432\u043e\u0433\u043e \u0442\u0438\u043f\u0430.<\/p>\n<p><em>Keywords<\/em>: distance learning, information technology, communication technology, Internet.<\/p>\n<p align=\"left\">\n<p><strong>DISTANCE LEARNINGAS INNOVATION TREND OF EDUCATION<\/strong><\/p>\n<p align=\"left\"><strong>Liudmila Khaymina, Evgeny Khaymin<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The paper analyses the necessity of transition from traditional learning to distance learning. One of the questions is to prepare teachers of new generation.<br \/><strong><br \/> Liudmila Khaymina<\/strong><br \/> <em>Associated Professor, Doctor on Pedagogy<\/em><br \/><em> Director Institute of Mathematics and Computer Science<\/em><\/p>\n<p><strong>Evgeny Khaymin<\/strong><br \/> <em>Senior Lecturer<\/em><br \/><em>Institute of Mathematics and Computer Science<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p align=\"left\"><strong><a id=\"c03\" name=\"c03\"><\/a>\u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0427\u041d\u0418 \u0421\u0420\u0415\u0414\u0421\u0422\u0412\u0410 \u0417\u0410 \u0420\u0410\u0417\u0420\u0410\u0411\u041e\u0422\u0412\u0410\u041d\u0415&nbsp;\u0418 \u0420\u0410\u0417\u041f\u0420\u041e\u0421\u0422\u0420\u0410\u041d\u0415\u041d\u0418\u0415 \u041d\u0410 \u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u041e \u0423\u0427\u0415\u0411\u041d\u041e<br \/> \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u0418 \u0421\u042a\u0417\u0414\u0410\u0412\u0410\u041d\u0415 \u0418 \u041f\u041e\u0414\u0414\u042a\u0420\u0416\u0410\u041d\u0415&nbsp;\u041d\u0410 \u041a\u0423\u0420\u0421\u041e\u0412\u0415 \u0417\u0410 \u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415<\/p>\n<p> \u0413\u0435\u043e\u0440\u0433\u0438 \u0422\u0443\u043f\u0430\u0440\u043e\u0432, \u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430<\/strong><\/p>\n<p align=\"left\"><strong><br \/> Abstract<\/strong>. \u0426\u0435\u043b \u043d\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u0434\u0430 \u0441\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u0442 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0437\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u0438 \u043f\u043e\u0434\u0434\u044a\u0440\u0436\u0430\u043d\u0435 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u0443\u0447\u0435\u0431\u043d\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u0438 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u0437\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u0412 \u043f\u044a\u0440\u0432\u0430 \u0447\u0430\u0441\u0442 \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d\u043e \u0443\u0442\u043e\u0447\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0438\u0442\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0438 \u0442\u0435\u0440\u043c\u0438\u043d\u0438 \u0438 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0437\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0443\u0447\u0435\u0431\u043d\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0437\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u0412\u044a\u0432 \u0432\u0442\u043e\u0440\u0430 \u0447\u0430\u0441\u0442 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0437\u0430 \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0435\u0442\u043e \u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0437\u0430 \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u043e\u0442\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435. \u0412 \u0442\u0440\u0435\u0442\u0430 \u0447\u0430\u0441\u0442 \u0441\u0435 \u0434\u0438\u0441\u043a\u0443\u0442\u0438\u0440\u0430 \u043e\u0431\u043d\u043e\u0432\u0435\u043d\u0430 \u0440\u0430\u043c\u043a\u0430 \u0437\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0437\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435.<\/p>\n<p><em>Keywords<\/em>: e-learning, LMS, LCMS, Learning objects, Framework for evaluation of LCMS<\/p>\n<p align=\"left\">\n<p><strong>TECHNOLOGICAL TOOLS FOR DEVELOPMENT, DELIVERING&nbsp;AND MAINTENANCE OF E-LEARNING CONTENT AND COURSES<\/strong><\/p>\n<p align=\"left\"><strong> <\/p>\n<p> Abstract.<\/strong> The aim of this paper is to be presented basic technological tools for development and maintenance of e-learning content and e-learning courses. In the first part we define terms used in the area of e-learning and present some popular tools and technologies for e-learning content development and delivering. In the second part the characteristics of Learning Management Systems (LMS) and Learning Content Management Systems (LCMS) are performed. At the end, we discuss updated framework for evaluation of e-learning environments.<\/p>\n<p><strong>Georgi Tuparov<\/strong><br \/> <em>Docent, PhD<\/em><br \/><em> Section \u201cSoftware tehcnolgogies\u201d, BAS<\/em><br \/><em> \u201cInformatics\u201d department, \u201cNeofit Rilski\u201d University, Blagoevgrad<\/em><\/p>\n<p><strong>Assoc. Prof. Dr. Daniela Dureva<\/strong><br \/> <em>Docent, PhD<\/em><br \/><em>\u201cInformatics\u201d department, \u201cNeofit Rilski\u201d University, Blagoevgrad<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p align=\"left\"><strong><a id=\"c04\" name=\"c04\"><\/a>\u0421\u041b\u0423\u0427\u0410\u0419\u041d\u041e \u0421\u042a\u0420\u0424\u0418\u0420\u0410\u041d\u0415 \u0412 \u0418\u041d\u0422\u0415\u0420\u041d\u0415\u0422<\/p>\n<p> \u0415\u0432\u0433\u0435\u043d\u0438\u044f \u0421\u0442\u043e\u0438\u043c\u0435\u043d\u043e\u0432\u0430<\/strong><\/p>\n<p align=\"left\"><strong><br \/> Abstract<\/strong>. \u0426\u0435\u043b\u0442\u0430 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u0434\u0430 \u043e\u0431\u044f\u0441\u043d\u0438\u043c \u0435\u0434\u043d\u0430 \u043e\u0442 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u0438\u0434\u0435\u0438 \u0437\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043d\u0430 \u043f\u043e\u0441\u0435\u0449\u0430\u0435\u043c\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 web \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0438\u0442\u0435. \u0429\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043c\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u043d\u0430 \u0435\u0437\u0438\u043a\u0430 C++, \u0437\u0430 \u0434\u0430 \u0438\u0437\u0443\u0447\u0438\u043c \u043c\u043e\u0434\u0435\u043b\u0430 \u043d\u0430 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0442\u043e \u0441\u044a\u0440\u0444\u0438\u0440\u0430\u043d\u0435. \u041c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044a\u0442 \u0435 \u0434\u043e\u0441\u0442\u044a\u043f\u0435\u043d \u0437\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043e\u0442 \u0441\u0440\u0435\u0434\u043d\u0438\u044f \u043a\u0443\u0440\u0441, \u0441 \u0431\u0430\u0437\u043e\u0432\u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0435\u0437\u0438\u043a\u0430 C++.<br \/><em><br \/> Keywords<\/em>: random surfer, web page ranking, stochastic simulation<\/p>\n<p align=\"left\"><strong><br \/> RANDOM INTERNET SURFING<\/strong><br \/><strong><br \/> Abstract<\/strong>. In this paper we describe the Random Surfer Model for evaluating the importance of web pages. Google computes PageRank of a particular page from the theoretical probability of visiting that page when clicking on links at random. We assume that the reader has some basic programming knowledge in C++ to follow and reproduce the idea of this model.<\/p>\n<p><strong>Eugenia Stoimenova<\/strong><br \/> <em>Professor, DSc in Mathematics<\/em><br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p align=\"left\"><strong><a id=\"c05\" name=\"c05\"><\/a>\u0418\u041d\u0414\u0418\u0412\u0418\u0414\u0423\u0410\u041b\u041d\u0410 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0410 \u0422\u0420\u0410\u0415\u041a\u0422\u041e\u0420\u0418\u042f&nbsp;\u0418\u0417\u0421\u041b\u0415\u0414\u0412\u0410\u041d\u0415 \u041d\u0410 \u0427\u0410\u0421\u0422\u0415\u041d \u0421\u041b\u0423\u0427\u0410\u0419<\/p>\n<p> Borislav Lazarov<\/strong><\/p>\n<p align=\"left\"><strong>Abstract<\/strong>. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u043e \u0435\u0434\u043d\u043e \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u0447\u0430\u0441\u0442\u0435\u043d \u0441\u043b\u0443\u0447\u0430\u0439: \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u0430 \u043f\u043e \u0438\u0437\u0433\u043e\u0442\u0432\u044f\u043d\u0435 \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043e\u0442 \u0443\u0447\u0435\u043d\u0438\u043a \u0432 \u0433\u043e\u0440\u043d\u0438\u044f \u043a\u0443\u0440\u0441. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d\u0430 \u0435 \u0438\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u044f, \u0440\u0435\u0433\u0438\u0441\u0442\u0440\u0438\u0440\u0430\u043d\u043e \u0435 \u0438\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442 \u043e\u0442 \u0441\u0438\u043d\u0442\u0435\u0442\u0438\u0447\u0435\u043d \u0442\u0438\u043f. \u0412 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442 \u043e\u0442 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441 \u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0432\u0430\u043d\u043e \u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u043d\u043e \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0441\u0440\u043e\u0447\u0435\u043d \u043f\u043b\u0430\u043d; \u0438\u0437\u0433\u0440\u0430\u0434\u0435\u043d\u0430 \u0435 \u0441\u0438\u043d\u0442\u0435\u0442\u0438\u0447\u043d\u0430 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442, \u0432 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442 \u043d\u0430 \u043a\u043e\u0435\u0442\u043e \u0441\u0430 \u043f\u043e\u0441\u0442\u0438\u0433\u043d\u0430\u0442\u0438 \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438.<\/p>\n<p><em>Keywords<\/em>: summarywise numbers, l<sub>1<\/sub>,l<sub>2<\/sub>,&#8230;,l<sub>k<\/sub> -summarywise numbers, syntheticcompetence, individual educational trajectory, Socratic style<\/p>\n<p align=\"left\">\n<p><strong>INDIVIDUAL EDUCATIONALTRAJECTORY \u2013 A CASE STUDY<\/strong><\/p>\n<p align=\"left\"><strong> <br \/> Abstract<\/strong>. The paper presents a case study: a particular student\u2019s activity dedicated to generalization of a problem from Chernorizec Hrabar Math Tournament. An individual educational trajectory has been developed that leads to forming student\u2019s competence of synthetic type. As a result of the applied medium-term educational strategy considerable increase of the student\u2019s activeness has been registered. Some new mathematical results have been obtained.<\/p>\n<p><strong>Borislav Lazarov<\/strong><br \/> <em>Associate Professor, Doctor in Pedagogy<\/em><br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>\n<p align=\"left\"><strong><a id=\"c06\" name=\"c06\"><\/a>\u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0427\u0415\u041d \u041c\u041e\u0414\u0415\u041b \u041d\u0410 \u0421\u042a\u0417\u0414\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u041c\u0423\u041b\u0422\u0418\u041c\u0415\u0414\u0418\u0419\u041d\u0418 \u041f\u0420\u0415\u0417\u0415\u041d\u0422\u0410\u0426\u0418\u0418 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 <br \/>\u041e\u0422 \u0423\u0427\u0415\u041d\u0418\u0426\u0418 \u0412 \u041e\u0421\u041c\u0418 \u041a\u041b\u0410\u0421 \u041f\u0420\u0418 \u0420\u0410\u0411\u041e\u0422\u0410 \u0412 \u0415\u041a\u0418\u041f<\/p>\n<p> \u041f\u0435\u0442\u044f \u0414\u0440\u0430\u0433\u0430\u043d\u043e\u0432\u0430,<\/strong><br \/><em>\u041f\u0413\u041b\u041f\u0418 \u201e\u0410\u0442\u0430\u043d\u0430\u0441 \u0411\u0443\u0440\u043e\u0432\u201d \u2013 \u0433\u0440. \u0413. \u041e\u0440\u044f\u0445\u043e\u0432\u0438\u0446\u0430<\/em><\/p>\n<p align=\"left\"><strong>Abstract<\/strong>: \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u043e\u0441\u043c\u0438 \u043a\u043b\u0430\u0441, \u0447\u0440\u0435\u0437 \u043a\u043e\u0439\u0442\u043e \u0434\u0430 \u0441\u0435 \u043f\u043e\u043c\u043e\u0433\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0434\u0430 \u043e\u0442\u043a\u0440\u0438\u044f\u0442 \u043f\u044a\u0442\u044f \u043a\u044a\u043c \u0441\u0435\u0431\u0435\u043f\u043e\u0437\u043d\u0430\u043d\u0438\u0435\u0442\u043e \u0438 \u0441\u0430\u043c\u043e\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u0430\u043a\u0442\u0438\u0432\u043d\u043e \u0443\u0447\u0435\u043d\u0435, \u0432\u044a\u0437\u043f\u0438\u0442\u0430\u0432\u0430\u043d\u0435 \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u043d\u043e\u0441\u0442 \u043d\u0430 \u043c\u0438\u0441\u043b\u0435\u043d\u0435\u0442\u043e \u0438 \u0440\u0430\u0437\u0432\u0438\u0432\u0430\u043d\u0435 \u043d\u0430 \u0443\u043c\u0435\u043d\u0438\u044f \u0437\u0430 \u0432\u0437\u0430\u0438\u043c\u043e\u043f\u043e\u043c\u043e\u0449 \u0432 \u0435\u043a\u0438\u043f\u043d\u043e \u0441\u044a\u0442\u0440\u0443\u0434\u043d\u0438\u0447\u0435\u0441\u0442\u0432\u043e. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0435\u0442\u0430\u043f\u0438\u0442\u0435 \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0435\u0437 \u043a\u043e\u0438\u0442\u043e \u043c\u0438\u043d\u0430\u0432\u0430\u0442 \u0447\u043b\u0435\u043d\u043e\u0432\u0435\u0442\u0435 \u043d\u0430 \u0435\u043a\u0438\u043f\u0438\u0442\u0435; \u043c\u044f\u0441\u0442\u043e\u0442\u043e \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0432 \u0435\u043a\u0438\u043f\u043d\u0430 \u0434\u0435\u0439\u043d\u043e\u0441\u0442 \u043f\u0440\u0438 \u0443\u0441\u0432\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u043d\u0430\u043d\u0438\u044f\u0442\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430; \u0435\u0442\u0430\u043f\u0438\u0442\u0435 \u043d\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0443\u043b\u0442\u0438\u043c\u0435\u0434\u0438\u0439\u043d\u0438\u0442\u0435 \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \u0438 \u0435 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u043d\u0430\u0447\u0438\u043d \u043d\u0430 \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0435\u043a\u0438\u043f\u0438\u0442\u0435 \u0438 \u0438\u0437\u0433\u043e\u0442\u0432\u0435\u043d\u0438\u0442\u0435 \u043e\u0442 \u0442\u044f\u0445 \u043f\u0440\u0435\u0437\u0435\u043d\u0442\u0430\u0446\u0438\u0438 \u0438 \u0441\u0438\u043c\u0443\u043b\u0430\u0446\u0438\u0438.<\/p>\n<p><em>Keywords<\/em>: integration of ICT in education, team work, stages in the creation of multimedia&nbsp;presentations by students in mathematics.<\/p>\n<p align=\"left\">\n<p><strong>TECHNOLOGICAL MODEL FOR CREATING MULTIMEDIA&nbsp;PRESENTATIONS IN MATHEMATICS BY STUDENTS TEAMWORK<\/strong><\/p>\n<p align=\"left\"><strong> <br \/> Abstract<\/strong>: This paper proposes a technological model of teaching mathematics in eighth grade, through which students are assisted to find their way to self-knowledge and selfeducation by active learning, cultivation of critical thinking and development of skills for providing mutual aid when working in teams. The paper reviews the stages of the learning process that team members go through it looks at the place of project training students in teams while learning mathematics, it presents the stages of creating multimedia projects and also, proposes a way for grading the teams\u2019 performance, presentations and the simulations prepared by the students.<\/p>\n<p><strong>Petya Draganova<\/strong><br \/> <em>teacher of mathematics and IT<\/em><br \/><em>PGLPI \u201eAtanas Burov\u201c<\/em><\/p>\n<p align=\"justify\">&nbsp;<\/p>\n<p class=\"style8\" align=\"right\"><span class=\"style9\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/span><span class=\"style9\"><br \/> <\/span><\/p>\n<hr align=\"left\" width=\"480\" \/>","protected":false},"excerpt":{"rendered":"<p>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0421\u042a\u0411\u0418\u0422\u0418\u042f \/ EVENTS \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0435\u043d \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u043b\u0430\u0434\u0438 \u0442\u0430\u043b\u0430\u043d\u0442\u0438\u201d 2012 [National Competition \u201cYoung&nbsp;Talents\u201d 2012] \/ \u0413. \u0414\u044f\u043d\u043a\u043e\u0432 \/ G. Dyankov &#8211; \u0441\u0442\u0440. 199 \u0421\u0443\u0431\u0435\u043a\u0442\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u043a \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [Subjectivity as a Methodological Principle in Informatization of Education] \/ \u0422. \u0421\u0435\u0440\u0433\u0435\u0435\u0432\u0430 \/ T. Sergeeva, \u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev &#8211; \u0441\u0442\u0440. 201 \u0414\u0438\u0441\u0442\u0430\u043d\u0446\u0438\u043e\u043d\u043d\u043e\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 [&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":[2882],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/press.azbuki.bg\/matematics\/matharticles\/math3-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0421\u042a\u0411\u0418\u0422\u0418\u042f \/ EVENTS \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0435\u043d \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u043b\u0430\u0434\u0438 \u0442\u0430\u043b\u0430\u043d\u0442\u0438\u201d 2012 [National Competition \u201cYoung&nbsp;Talents\u201d 2012] \/ \u0413. \u0414\u044f\u043d\u043a\u043e\u0432 \/ G. Dyankov &#8211; \u0441\u0442\u0440. 199 \u0421\u0443\u0431\u0435\u043a\u0442\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u043a \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [Subjectivity as a Methodological Principle in Informatization of Education] \/ \u0422. \u0421\u0435\u0440\u0433\u0435\u0435\u0432\u0430 \/ T. Sergeeva, \u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. 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